Author: paulpatenaude

Paul Patenaude a une expérience de plus de 35 années dans l'enseignement et l'animation pédagogique en mathématiques au primaire et au secondaire, au Québec et à l'étranger. Il est auteur ou co-auteur de nombreux ouvrages dédiés à l'enseignement des mathématiques dont ce lexique des termes utilisés avec les jeunes de 5 à 17 ans. Il peaufine ce lexique depuis plus de 30 ans. Prix d'excellence du GRMS (prix Claude Janvier) en 1997, prix du meilleur article de la revue l'Envol du GRMS (prix Euler) en 1992. Il adore voyager et a déjà exploré de nombreux pays sur les cinq continents, curieux à la fois des cultures et de l'histoire. Il apprécie recevoir vos commentaires et vos questions auxquelles il s'empressera de répondre.

Deficient Number

Whole number for which the sum of its proper divisors is less than the number itself. Examples Consider the number 81. The sum of its proper divisors is 40, because: 1 + 3 + 9 + 27 = 40. Because 40 < 81, this means that 81 is a deficient number. Consider the whole number [...]

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Denominate Number

Number associated with what it counts, evaluates, measures, quantifies, or describes in any way. In some ways, a denominate number is a number-of something. Examples A temperature is usually represented by a denominate number, for example: 10 °C. A size is often expressed by a denominate number, for example: 172 cm. A measurement is not a [...]

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Figurate Number

Cardinal of a set of points that can be arranged in a regular way on a given geometric shape. Historical Note Figurate numbers have been a concern for mathematicians from earliest Antiquity. Pythagoras was interested in the connections between these numbers and arithmetic and geometry. Plato later continued Pythagoras' work. See also : Square number Cube number [...]

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Perfect Number

Whole number for which the sum of its proper divisors is equal to the number itself. Examples Consider the number 496. The sum of its proper divisors is 496, because: 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496. Therefore, 496 is a perfect number. [...]

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Triangular Number

Number that we obtain by adding the first n non-zero whole numbers. Figurate number that can be represented by a triangle or a sequence of interlocked triangles. The sequence of triangular numbers is: 1, 3, 6, 10, 15, ....\(\dfrac {n\left( n+1\right) } {2}\) where \(n\) represents both the rank of the term in the sequence and [...]

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Congruent Numbers Modulo N

Integers a and b for which the difference is a multiple of the number n. We also say that a and b are congruent modulo n if they have the same remainder after division by n. Examples The numbers 9 and 21 are congruent modulo 12, as we can see in the notation system for [...]

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Number

A mathematical object that represents quantities, positions, sizes, measurements, etc. We often tend to confuse number and digit, particularly in radio, television, and advertising communications, which is an error. In fact, digits are graphic characters that allow us to write numbers. In our number system, there are ten digits, which are 0, 1, 2, 3, [...]

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Abundant Number

Whole number for which the sum of its proper divisors is greater than the number itself. All whole numbers can be classified in one of these three classes: Abundant numbers, Perfect numbers, Deficient numbers. Examples Consider the whole number 20. The sum of its proper divisors is 22, like this: 1 + 2 + 4 + 5 [...]

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Square Number

Figurate number that we can represent by a square or a sequence of interlocked squares. The sequence of square numbers is: 1, 4, 9, 16, … n2 where n represents both the position of the term in the sequence and the number of points on the largest square in the figure. Educational Note The number [...]

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Cube Number

Figurate number that we can represent by a cube or a sequence of interlocked cubes. The sequence of cube numbers is: 1, 8, 27, 64, …, n³ where n represents both the rank of the term in the sequence and the number of points on the largest cube in the figure. Educational Notes It’s important to note [...]

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Chromatic Number

Minimum number of different colours needed to colour all of the vertices in a graph so that two adjacent vertices are different colours. The initial results of graph colouration concern planar graphs almost exclusively: it consists of colouring maps. Since the end of the 19th century, mathematicians have demonstrated that it only takes 4 colours [...]

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Transcendental Number

Complex number that is not algebraic. A transcendental number is a real or complex irrational number that cannot be expressed as the root of a polynomial equation. Examples The numbers π and e are real irrational transcendental numbers. The number \(2^{\sqrt{2}}\) is also a real transcendental number. The number \(\sqrt{5}\) is an irrational number, but [...]

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Periodic Number

Expression used to refer to a number whose decimal notation is repeating. It includes rational numbers where the decimal expansion does not have 0 or 9 as a period. Symbol The period of a number with a repeating decimal is noted with a horizontal line above the sequence of digits that repeats: \(\dfrac{2}{13} = 0.153\space846\space153\space846 ... = [...]

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Positive Number

Real number that is greater than or equal to zero. The only number that is both positive and negative is the number 0. In general, the sign of a positive integer is implied and we do not write it. The opposite of a positive number is a negative number with the same absolute value and [...]

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Prime Power

Number that can be expressed as the power of one single prime number. Prime powers are commonly used when we factor a number or when we determine the GCD or the LCM of two or more numbers. Examples 72 = 23 × 32 32 = 25 200 = 23 × 52 PGCD (72, 32, 200) = 23 = 8 PPCM(72, 32, 200)  = 25 × [...]

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Rational Number

Number that can be expressed in the form of the quotient of two integers a and b where b is not zero. Rational numbers can be written in different forms, including fractional notation, decimal notation and percentage notation. Symbol The symbol used to represent the set of rational number is the letter \(\mathbb{Q}\). Examples Any [...]

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Real Number

Number that, when written in decimal notation, is an unlimited decimal sequence periodic or not. Notations The symbol that represents the set of real numbers is the letter \(\mathbb{R}\). The symbol that represents the set of real positive numbers is: \(\mathbb{R}_{+}\) = {x ∈ \(\mathbb{R}\) | x ≥ 0} The symbol that represents the set of real [...]

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Prime Number

Whole number that is greater than 1 and that has exactly two distinct divisors, which are 1 and itself. Whole number greater than 1 that has exactly two distinct whole divisors. Properties There is an infinite number of prime numbers. By definition, the numbers 0 and 1 are neither prime nor composite. A whole number [...]

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Irrational Number

Real number that cannot be written in the form of the ratio \(\frac {a}{b}\) where \(a\) and \(b\) are integers and \(b\) ≠ 0. Symbols The symbol \(\mathbb{Q'}\) represents the set of irrational numbers and is read as "Q prime". The symbol \(\mathbb{Q}\) represents the set of rational numbers. Combining rational and irrational numbers gives the set of real [...]

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Whole Number

 

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Negative Number

Real number that is less than or equal to zero. The only number that is both positive and negative is the number 0. The opposite of a positive number is a negative number with the same absolute value and vice versa. The opposite of –5 is 5. The opposite of 7 is –7. Examples The [...]

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Ordinal Number

Number that makes it possible to determine the position of someone or something in a given context. Non zero whole-number that indicates the place occupied by an element in a set when the elements are arranged in a certain order. Notation To represent an ordinal number, we use a numerical adjective: first, second, third, fourth, [...]

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Even Number

Number in which the ones digit is 0, 2, 4, 6 or 8. Integer that is divisible by two. Integer that is a multiple of 2. Examples The sequence of even whole numbers is: {0, 2, 4, 6, 8, 10, 12, 14, ...} The set of even integers is: {..., –8, –6, –4, –2, 0, [...]

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Palindromic Number

Number that can be read in both direction, which means that the sequence of digits is the same when it is read from right to left or from left to right. In everyday language, there are palindromic words like NON, ANNA, LAVAL and KAYAK. Examples The numbers 66, 161, 1441 and 580 085 are palindromic [...]

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Golden Ratio

Limit of the ratio of two consecutive terms in the Fibonacci sequence. An approximate value of this number is 1.618 033 989. The golden ratio is sometimes called the divine proportion. This number is generally represented by the Greek letter φ (phi</em). Example The golden ratio is the algebraic number that is the real positive [...]

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Integer

Number that belongs to the set \(\mathbb{Z}=\left\{ \ldots ,-3,-2,-1,0,1,2,3,\ldots \right\}\). Positive or negative number for which the absolute value is a whole number. Synonym of relative integer. The set of integers is: \(\mathbb{Z} = {..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}\). Symbols The set of integers is represented by the letter [...]

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Mixed Number

Rational number that is written as a whole number and a fraction. Example \(5 \frac{1}{2}\) is a mixed number. The integer is 5 and the fraction is \(\frac{1}{2}\).

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Imaginary Number

Complex number where the real part is zero and the imaginary part is not zero. Number of the form bi where b ≠ 0. Examples \(\sqrt{−1}\) is an imaginary number. \(5\sqrt{−7}\) is an imaginary number.

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Odd Number

Number where the ones digit is 1, 3, 5, 7 or 9. Integer that is not divisible by two. Number that is a multiple of 2 minus one. Number in the form (2n + 1) or (2n – 1) where n ∈ \(\mathbb{Z}\). Examples The sequence of odd whole numbers is: {1, 3, 5, 7, 9, [...]

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Decimal Number

Number in which the whole part is separated from the decimal part by a decimal point. Decimal numbers are real numbers written in decimal notation. Examples The expression \(\frac{2}{3}\) represents a real number where the whole part is 0 and the decimal part is 0.666 666 … The expression \(\frac{7}{4}\) represents a real number where [...]

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Composite Number

Whole number that is greater than 1 and that has more than two distinct divisors. The number 0 and 1 are not composite numbers. The list of composite numbers under 25 is: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24. Properties All composite number can be expressed in a [...]

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Random Number

Number that is chosen by chance. Example We are randomly drawing one marble from a jar containing 100 marbles numbered 1 to 100. This experiment is a random experiment. The number drawn is therefore a random number.

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Cardinal Number

The cardinal of a set is the number of elements in a set. Expression that is sometimes used to refer to the class of sets equipotent to a given set. A cardinal number is a number that characterizes the quantity of elements in a set, as opposed to the ordinal number that characterizes a rank [...]

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Complex Number

Number that can be written in the form a + bi where a and b are real numbers and i2 = −1. In this kind of notation, the number a is called the real part and the number b is called the imaginary part of the complex number. The set of real numbers is a [...]

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Multiplier

In a multiplication, name given to the number by which we multiply. Examples In the multiplication 5 × 9 = 45, the number 5 is the multiplicand, the number 9 is the multiplier and the number 45 is the product. We can also say that the numbers 5 and 9 are factors. In the multiplication [...]

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Multiplication

Operation that, to each pair of numbers called the factors of the multiplication, associates a new number called the product of these factors. The inverse operation of multiplication is division. Symbol The symbol of multiplication is "×" which is read as "multiplied by". Properties (a) Multiplication is a commutative operation. Example : 12 × 15 = [...]

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n-tuple

Ordered list in the form (x1, x2, ..., xn) where xi represent elements of a perfectly defined set. Examples The coordinate pair (2, 5) is an n-tuple of order 2. An n-tuple of order 3, such as (2, 5, 7) is called a triplet. The next orders are called: quadruplet, quintuplet, sextuplet, etc. Etymological Note [...]

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Node

Name given to each vertex in a network. Example Points A, B, C, D, E, F and G are the nodes in this network:

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Negation

The negation of a proposition P, is the proposition noted as "¬P", "non P" that is true when the proposition P is false and false when the proposition P is true. Examples ¬(P ∧ Q) = ¬P ∨ ¬Q ¬(P ∨ Q) = ¬P ∧ ¬Q ¬(P → Q) = P ∧ ¬Q See also : Conjunction Disjunction [...]

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Mean Proportional

In a proportion with three terms, the mean term is the mean proportional between the two other terms. The expression "mean proportional" is a synonym of "geometric mean". Example Consider this proportion: \(\dfrac{2}{x}\) = \(\dfrac{x}{8}\) The term \(x\) is a mean proportional. We can calculate it with the geometric mean : \(\overline{x}_g\) = \(\sqrt[2]{2 × 8}\) = \(\sqrt[2]{16} = [...]

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Multiple

An integer \(N\) is a multiple of an integer \(n\) if there is an integer \(a\) for which \(N = n × a\). If the number \(N\) is a multiple of a non-zero number \(n\), then the number \(n\) is a divisor of the number \(N\). Properties All integers are multiples of 1 and themselves: 7 = 7 × 1. [...]

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Multiplicand

In a multiplication, name given to the number to multiply by the other. Examples In the multiplication 5 × 9 = 45, the number 5 is the multiplicand, the number 9 is the multiplier and the number 45 is the product. We can also say that the numbers 5 and 9 are the factors in [...]

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Geometric Mean

The \(n\)-th root of the product of \(n\) values in a distribution of a quantitative statistical characteristic. Notation Because the geometric mean is a different measure from the arithmetic mean, we use the notation \(\overline{x}_g\) to designate the geometric mean of a distribution. Some authors also use G or \(\overline{x}^{G}\). The geometric mean of two [...]

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Weighted Mean

If E is a set of numerical statistical data, P is a set of weights and R is a function of E in P that associates a weight to each value of E in P, then the weighted mean of the data in E is the quotient of the products of E × P by [...]

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Arithmetic Mean

Quotient of the sum of the values in the distribution of a quantitative statistical characteristic by the number of values. Notations The arithmetic mean of a distribution is noted as: \(\overline{\textrm{x}}\). Some books prefer the notation \(\overline{\textrm{X}}\). When it is necessary to distinguish between the mean of an entire population and the mean of a sample, [...]

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Base Element

Drawing used as a base object to produce repeated congruent figures to cover a surface, like a tessellation, or to create a border, like a frieze, or set of numbers used to suggest a numerical sequence. The repetition of a base element is a synonym of pattern or sequence. Example In the number sequence 1, 2, [...]

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Number Pattern

Synonym of numerical sequence.

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Minimum of a Function

A function \(f\) defined on a subset E of real numbers has a minimum m at a point \(a\) in E if m = \(f(a)\) and if, for all \(x\) in E, \(f(x)\) is greater than or equal to \(f(a)\). Therefore, m is the minimum of the set of images of f. Example Consider the function defined by \(f(x)\) = [...]

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Mode

Value that has the greatest frequency in the distribution of a discrete quantitative characteristic. Notation The symbol for mode is "Mod" which is read as "mode". The mode is a measure of central tendency. A distribution can have several modes. A distribution in which all of the values have the same frequency does not have [...]

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Modality

Possible response or attribute of an element in a distribution of a qualitative statistical attribute. Example In this bar graph, the modalities of the study are the different modes of transportation: car, bus, bike, walking, and other.   See also: Mode Qualitative statistical attribute

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Billion

One thousand groups of one million units, in the decimal number system. Notations The number 64 000 000 000 is read as "sixty-four billions". One billion is written as "1 000 000 000" or "\(10{^9}\)". Examples In the number 64 789 000 000, there are 64 billions. In the number 64 789 000 000, the [...]

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Millesimal Number

Number that refers to a year. Example The 2010 World Expo took place in Shanghai. The number 2010 is the millesimal number of the year of this exhibition.

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Millilitre

Unit of measurement of capacity equal to one-thousandth of a litre. Notations The symbol for millilitre is “ml” which represents “millilitre.” The symbol for microlitre is “μl” which represents “microlitre.” One litre is equal to 1000 millilitres and we write: 1 L = 1000 ml. One millilitre is equal to 1000 microlitres and we write: [...]

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Millimetre

Unit of measure of length equal to one-thousandth of a metre. Notations The symbol is “mm” which represents “millimetre.” One metre is equal to 1000 millimetres and we write: 1 m = 1000 mm. One millimetre is equal to one-thousandth of a metre and we write: 1 mm = 0.001 m. One millimetre is equal [...]

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Million

 

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Quantitative Method

Mathematical tool or strategy (model) which is intended for the description of quantifiable, measurable facts. Quantitative methods are based on two indissociable elements: the methods, the data processed using these methods. The methods are intended to describe facts. These methods are referred to as descriptive statistics. They can also focus on verifying theoretical elements; this consists [...]

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Measure of Central Tendency

Number that represents the centre of a distribution and the position of the various values of the distribution in relationship to this centre. The main measures of central tendency are arithmetic mean, median and mode. Example This distribution provides a list of the ages of 25 students in a grade 6 class. 10, 10, 11, [...]

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Square Metre

Unit of measure of surface that corresponds to the area of a square with 1 metre sides. The square metre is a unit of measurement that is used to calculate area (the area being the measure of the surface considered). Properties One square metre is equal to 100 square decimetres and we write: 1 m\(^{2}\) [...]

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Cubic Metre

 

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Measure of Dispersion

 

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Maximum of a Function

A function f defined on a subset E of real numbers has a maximum M at a point a in E if M = f(a) and if, for all x in E, f(\(x\)) is less than or equal to f(a). Therefore, M is the maximum of the set of images of f. Example Consider the [...]

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Mass

Quantity of matter of an object. Mass is the property of an object to be more or less heavy. The mass of an object only depends on its volume and the materials that form the object. The mass of an object does not vary based on the location in the universe where we measure it. [...]

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Margin of Error

In a statistical study focusing on a quantitative characteristic, an estimation of the range of the results or values obtained during a survey, assuming that we redo the same operation several times. The greater the margin of error, the less we can trust that the results of the survey are close to the real results, [...]

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Law

Relationship or property. Sometimes a synonym for rule. Examples Addition in the set of whole numbers is an internal composition law in \(\mathbb{N}\). Division in the set of integers is not an internal composition law in \(\mathbb{N}\) because the results obtained are not all elements of \(\mathbb{N}\). The multiplication of a vector by a real number (scalar) is [...]

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Litre

Unit of measure of capacity in the International System of Units (SI). Notation The symbol for litre is “L” which represents “litre.” We use this symbol instead of the lowercase letter l to avoid any possible confusion with the digit 1. For the multiples and sub-multiples of a litre, we use the lowercase letter, such [...]

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Limit of a Variable

A fixed magnitude that a variable infinitely approaches. Examples The following sum has a limit of 2 : 1 + \(\frac{1}{2}\) + \(\frac{1}{4}\) + \(\frac{1}{8}\) + \(\frac{1}{16}\) + \(\frac{1}{32}\) + ... The following sequence converges to 2 : 2 + \(\frac{1}{2}\), 2 – \(\frac{1}{2}\), 2 + \(\frac{1}{3}\), 2 – \(\frac{1}{3}\), ... See also: Statistics class limit Limit of a function [...]

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Lemma

In the context of formal argumentation, proposition deduced from one or more axioms, the demonstration of which paves the way for the demonstration of a theorem that will follow. Etymological Note The word lemma comes from the Greek word lêmma (λημμα)that means "result" or “received” or even, by extension, "consequence". In a mathematical context, the [...]

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Statistical Relationship

Connection between two statistical characteristics. In a statistical survey, we say that there is a statistical relationship between two variables studied in this survey if we can determine a connection (linear or not) between these variables. This relationship is a general model that allows us to better describe the phenomenon observed and predict new results [...]

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Kilogram

Unit of measure of mass that is equivalent to 1000 grams. One kilogram is equivalent to about 2.204 622 62 pounds. One kilogram is equivalent to the mass of one litre of pure water at 4°C. Notation The expression “1 kg” is read as “one kilogram. One kilogram is equivalent to 1000 grams and we [...]

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Kilometre

Unit of measure of length that is equivalent to 1000 metres. One kilometre is equivalent to about 0.621 371 10 miles. Kilometre is a multiple of metre that is most frequently used to measure distances (for example: between cities). We define the kilometric points along communication channels, which appears on roads as road boundary markers [...]

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Square Kilometre

Unit of measure of surface that is equivalent to the area of a square with sides that are each one kilometre long. Notation We write: 1 km\(^{2}\) = 1 000 000 m\(^{2}\), because 1000 × 1000 = 1 000 000.

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Inverse of a Number

Two numbers are inverses of each other when their product is 1. Examples The inverse of 2 is \(\dfrac{1}{2}\) since \(2 × \dfrac{1}{2} = 1\). The inverse of \(\dfrac{2}{3}\) is \(\dfrac{3}{2}\) since \(\dfrac{2}{3}\) × \(\dfrac{3}{2} = 1\).

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Congruent

Having the same measure Symbol The relationship of congruence between two geometric objects is represented by the symbol \(≅\) which is read as “is congruent to.” Example In this example, the two triangles are congruent. Therefore, we can write: Δ ABC \(≅\) Δ A’B’C’.

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Invariant

Term that refers to a property or a set that is preserved under the effect of a relation. A set E is generally invariant by a relation ℜ if ℜ(E) = E. Examples Invariant set: In a reflection, the line of reflection is an invariant line (fixed line) for this transformation. In a rotation, the centre of [...]

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Isometry

Geometric transformation that preserves the measures of the figures (lengths, angles) or distances. The word isometry also refers to the property of that which is isometric. We can determine the isometry of two figures by examining the measures of their sides and their corresponding angles. Properties A direct isometry preserves the orientation of the plane. Translations and [...]

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Compound Interest

Earnings that is seen as payment for an investment or a price to pay for borrowing a sum of money, in the case where the earnings are periodically added to the previous capital or balance. Compound interest is often expressed in the form of a percentage of the borrowed sum to which the previous interest [...]

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Interpolation

Operation that consists of constructing or estimating the value of a function for a value of the variable taken between two discrete values in the interval in which the relationship was established. Example Starting from the values of \(\log(5)\) and \(\log(6)\), we can estimate using interpolation the value of \(\log(5.5)\): \(\log(5.5) ≈ \log(5) +\dfrac{\log(5) + [...]

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Confidence Interval

A confidence interval makes it possible to define a margin of error between the results of a survey and an exhaustive summary of the entire population. More generally, the confidence interval makes it possible to assess the precision of the estimate of a statistical parameter on a given sample. Example Consider E = {x1,..., xn} [...]

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Interior of a Conic Section

Set of points on a plane from which no tangents can be drawn to a conic section. The interior of a hyperbola is the region where the foci are located. Example The orange portion of the graph below illustrates the interior of a hyperbola with the equation \(\dfrac{x^2}{4} − \dfrac{y^2}{7} = 1\), that is, the region [...]

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Logical Implication

The implication of Q by P is the proposition (¬P) ∨ Q, noted as "P ⇒ Q" or "P implies Q" which is false only if the proposition P is true and the proposition Q is false. The implication is true in all other cases. Symbol The symbol of a logical implication is "P ⇒ [...]

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Logical Identity

Given two propositions P and Q, the identity of P and Q, noted as P ⇔ Q or "P if and only if Q", is the new proposition that is true if and only if the biconditional P ↔ Q is a tautology. The logical identity is also called logical equivalence and so the propositions P are Q [...]

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Hypothesis

An already established statement that is a baseline to demonstrate a new proposition. Examples The definitions, axioms and theorems associated with a theory can be considered to be the hypotheses in the demonstration of a new property.

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Histogram

Diagram that uses juxtaposed bars to represent the distribution of a continuous quantitative statistical attribute on a given sample. For each class, we draw a rectangle for which the side along the x-axis has a width that is the amplitude of the statistical class and for which the area is proportional to the frequency of each [...]

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Hectare

Unit of area that is equivalent to 10 000 \(\textrm{m}^{2}\), or a square with 100-metre sides. Notation The notation used to represent a hectare is “ha”. The hectare is a multiple of an are which equals 100 \(\textrm{m}^{2}\). It is equivalent to one square hectometre. This unit of measurement is generally used to measure the [...]

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Hectolitre

Unit of measurement of capacity equal to 100 litres. This unit of measurement is commonly used in the agri-food sector. Notation The notation used is “hl” which represents “hectolitre.” One hectolitre is equal to 100 litres and we write: 1 hl = 100 L. Etymological Notee Adopted in 1795, the prefix for this unit comes [...]

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Hectometre

Unit of measurement of length equivalent to 100 metres. Notation The notation used is “hm” which represents “hectometre.” One hectometre is equal to 100 metres and we write: 1 hm = 100 m. Example You may have noticed that on most highways, between each kilometre, there is a boundary marker every 100 metres, or in [...]

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Cluster

In a scatter plot, set of data grouped around a central datum that is representative of the set of the distribution. In a distribution, a cluster forms a homogeneous set without gaps.

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Valued Graph

Graph in which a real positive number (value) is assigned to each edge. Example This is a valued graph, because we assigned a value to each edge: The chain of edges that connect the vertices A-B-G-H-E-D in order has a value of 16. The weight of the edge CD is 4.

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Group

Name given to an algebraic structure (G, ⊕) formed by a set G in which we defined an operation noted here as ⊕ responding to the following conditions: G has an identity element n for the operation ⊕; each element x of G has a symmetric x ' in G such as x ⊕ x ' = n. Properties Abelian group [...]

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Height

Dimension of an object from its base to its vertex. The word height often refers to the measure of this dimension or to the segment that represents it. In a right rectangular prism, the height is a quantity that measures the third dimension of this prism. The dimensions of the base of a right rectangular [...]

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Directed Graph

Graph in which each edge connecting two vertices is directed (has a sense). The edges of a directed graph are called arcs. Example This is a directed graph, because each arc is directed. On a map, the city street plan is generally represented by an undirected graph. However, if there are several one-way streets, the [...]

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Open graph

Graph in which there is at least one vertex with degree equal to one. Example This is an open graph, because the vertex G has a degree equal to 1:

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Planar Graph

Graph that can be placed on a plane in such a way that the edges only intersect at their endpoints. Trees are planar graphs. Examples This is a planar graph: This tree is a planar graph:

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Weighted Graph

Synonym for valued graph.

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Regular Graph

Graph in which all the vertices have the same order. A graph is regular if all its vertices have the same degree. Example This graph is regular, because all its vertices are degree 3:

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Simple Graph

Graph in which each pair of vertices is connected by one edge at most and no vertices have any loops. Example This is a simple graph. It does not have any loops:

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Proportional Quantities

Two quantities are said to be proportional or directly proportional if their measurements evolve in the same direction. In other words, two quantities are proportional if we can calculate the measurement of one by multiplying (or dividing) the measurement of the other by the same number. This number is called the coefficient of proportionality of [...]

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Graph (Graph Theory)

Mathematical model in which a set of objects, represented by points called vertices, are connected to one another by links, represented by lines or dashes called arcs or edges. The vertices are labelled. A graph is therefore made up of two sets: on the one hand, set E of the edges and on the other hand, set [...]

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Complementary Graph

Sub-graph of a given graph that includes all the missing edges for this graph to be complete. Example Consider graph G below, which is a complete graph: If we consider the sub-graph E of G including the edges {AB, AE, BC, CD, DF, EF}, then the complementary graph of E, noted as E’, is the [...]

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Complete Graph

Graph in which any two vertices are connected by at least one edge. A complete graph is a simple graph in which all the vertices are adjacent, which means that every pair of vertices is connected by an edge. A complete graph is a simple graph in which all possible edges appear. Example This is [...]

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