## Algebra

Algebra is a branch of mathematics that uses letters or symbols as a place holder for unknown values or numbers.  These variables are used to represent relationships and to solve equations.

### Science Branches

Science
Formal Science
Mathematics
Pure Mathematics
Algebra
• Abstract Algebra
• Associative Algebra
• Category Theory
• Differential Algebra
• Elementary Algebra
• Group Theory
• Homological Algebra
• Field Theory
• Lattice Theory
• Order Theory
• Lie Algebra
• Linear Algebra
• Multilinear Algebra
• Non-associative Algebra
• Ring Theory
• Universal Algebra

## Algebra Glossary

### A

• Absolute Value  -  Makes a negative number positive  $$\large{ \left\vert -x \right\vert = x }$$  and positive numbers and  $$\large{ 0 }$$  are not changed.
• Addend  -  Any one of a set of terms  $$\large{ 3 + 7 = 10 }$$  to be added.  $$\large{ 3 }$$  and  $$\large{ 7 }$$  are each addends,  $$\large{ 10 }$$ is the sum.
• Algebraic Expression  -  Includes variables, if not, then it is called an arithmetic expression.  Equation is $$\large{13a^2 + 7x = 18 }$$  The variables are $$\large{ a }$$ and $$\large{x }$$ .
• Algebraic Properties  -
• A postulate is a statement that is assumed true without proof.
• A theorem is a true statement that can be proven.
• Associative Property  -  How you group the numbers does not matter.  $$\large{ \left(a+b\right)+c = a+\left(b+c\right) }$$  or  $$\large{ \left(a\;b\right)\;c = a\; \left(b\;c\right) }$$
• Axes  - A horizintal number line, x-axis and a vertical number line, y-axis.  Both used on a coordinate system or graph.
• Axiom  -  A statement accepted as true without proof.

### B

• Base  -  The term  $$\large{13a^2 }$$  has a base  $$\large{ a }$$ .
• Binary Number  -  Use only the digits $$\large{ 0 }$$ and $$\large{ 1 }$$ .
• Binomial  -  A polynomial with only two term  $$\large{ 13a^2+7x }$$ .

### C

• Coefficient  -  A number multiplied by a variable.  An equation  $$\large{13a^2+7x-21=19 }$$ , the coefficients are  $$\large{13, 7 }$$ .
• Combination  -  A set of objects in which the order is not important.  $$\large{ \left(7, 21, 19\right) }$$  or  $$\large{ \left(19, 7, 21\right) }$$
• Common Demoninator  -  Two or more fractions  $$\large{ \frac{3}{8} + \frac{7}{8}}$$  that have the same denominator  $$\large{ 8 }$$ .
• Common Difference  -  $$\large{ 3 }$$  is the difference between each number  $$\large{ 3, 6, 9, 12, ... }$$  in a sequence  $$\large{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ... }$$ .
• Common Factor  -  The factors of two or more numbers that have some factors that are the same (common) in each.
• Common Fraction  -  A fraction where both numbers  $$\large{ \frac{3}{4}, \frac{7}{8} }$$  top and bottom are integers.
• Common Multiple  -  Two or more numbers that have the same multiple.
• Common Ratio  -  A number multipling the previous term in a geometric sequence.  Series  $$\large{ 3, 6, 12, 24, ... }$$  with a common rario of 2.
• Commutative  -  When the order of the numbers do not matter.  Works for addition and multiplication but not for subtraction or division.    $$\large{ 3 + 7 = 7 + 3 }$$  or  $$\large{ 3\; x\; 7 = 7\; x\; 3 }$$
• Commutative Property  -  The moving aroung of the numbers using  $$\large{ + }$$  of  $$\large{ \times }$$  does not matter.  $$\large{ a + b = b + a }$$  or  $$\large{ a \; b = b \; a }$$
• Comparison  -  Compasring two numbers to see which is the largest.
• Complex Fraction (Compound Fraction)  -  A fraction where the denominator, numerator or both contain a fraction.  $$\large{ \frac{ 5 }{ \frac{7}{8} } }$$ ,  $$\large{ \frac{ \frac{3}{8} }{ 9 } }$$ ,  $$\large{ \frac{ \frac{3}{8} }{ \frac{7}{8} } }$$
• Complex Number  -  A combination of a real  $$\large{3, \frac{3}{4}, 13.45, -3.56, ... }$$  number and imaginary  $$\large{\sqrt{-1} = i }$$  number for a result of  $$\large{x + y\;i }$$ .   $$\large{ x }$$  is the real part and  $$\large{ y }$$  is the imaginary part.
• Composite Number  -  A positive integer number  $$\large{ 4, 6, 8, 9,... }$$  that has factors other than  $$\large{ 1 }$$  and the number itself.
• Compute  -  To compute  $$\large{ 3-2 }$$  is to figuring out the answer  $$\large{ 1 }$$ .
• Conjugate  -  Is when you change the sign.  from  $$\large{ a+b }$$  to  $$\large{ a-b }$$,  from  $$\large{ 3a-4b }$$  to  $$\large{ 3a+4b }$$  $$\large{ ,... }$$
• Consecutive Number  -  Numbers that follow each other in order, from smallest to largest.  $$\large{ 15, 20, 25, 30, 35, ... }$$
• Constant  -  The term expressed with no variables.  An equation  $$\large{13a^2+7x-21=19 }$$ , the constants are  $$\large{21, 19 }$$ .
• Conversion  -  The act of changing a unit to a different unit of measure.
• Counting Number  -  Any number used to count things  $$\large{ 1, 2, 3, 4, 5, 6,... }$$  excluding  $$\large{ 0 }$$ , negative numbers, fractions or decimals.
• Cube Number  -  $$\large{ 5 \times 5 \times 5 = 125 }$$ ,  $$\large{ 125 }$$ is the cube number.
• Cube Root  -  $$\large{ ^3\sqrt{125} = 5 }$$ ,  $$\large{ 5 }$$ is the cube root.

### D

• Decimal Number  -  Based on 10 digits.  $$\large{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }$$
• Denominator  -  The number of equal parts of the whole is  $$\large{ 8 }$$ , fraction is  $$\large{ \frac{3}{8} }$$ .
• Digit  -  A numeral  $$\large{ 2119 }$$  has digits  $$\large{ 2, 1, 1, }$$  and  $$\large{ 9 }$$ .
• Disjoint Event (Mutually Exclusive)  -  Events that have no outcomes in common.
• Distributive Postulate  -  Let $$\large{ a }$$ , $$\large{ b }$$ and $$\large{ c }$$ be real numbers.  $$\large{\;a \left (b + c \right ) = ab + ac\; }$$
• Distributive Property (Distribution)  -  Multiply the parts of an expression  $$\large{ a \left(b-c \right) }$$  into another expression  $$\large{ a\;b-a\;c }$$ .
• Dividend  -  In a set of terms  $$\large{ 3 \div 7 = 0.43 }$$  the amount to be divided.  $$\large{ 3 }$$  is the dividend,  $$\large{ 7 }$$  is the divisor, and  $$\large{ 0.43 }$$  is the quotient.
• Divisor  -  In a set of terms  $$\large{ 3 \div 7 = 0.43 }$$  the number divided by.  $$\large{ 7 }$$  is the divisor,  $$\large{ 3 }$$  is the dividend, and  $$\large{ 0.43 }$$  is the quotient.
• Division Postulate  -  A postulate is a statement that is assumed true without proof.  Let $$\large{ a, b, c }$$ be real numbers.  If $$\large{ a=b }$$ and $$\large{ c \ne 0 }$$, then $$\large{ \frac{ a }{ c } = \frac{ b }{ c } }$$ .
• Domain of a Function  -  A set of values for the independent variable that makes the function work.

### E

• Element  -  Anything contained in a set.
• Elementary Algebra  -  Performs basic concepts of algebra operations.
• Engineering Notation  -  A way of writing large numbers  $$\large{ 1 2 3, 0 0 0 }$$  into smaller numbers  $$\large{ 1 2 3 \cdot 10^3 }$$  where the power of 10 is multiplied by 3.
• $$\large{\; 1 2 3 4. 5 = 1. 2 3 4 5 \times 10^3}$$
• $$\large{\; 1 2 0 = .1 2 \times 10^3}$$
• $$\large{\; 1, 2 0 0 = 1. 2 \times 10^3}$$
• $$\large{\; 1 2, 0 0 0 = 1 2 \times 10^3}$$
• $$\large{\; 1 2 3, 0 0 0 = 1 2 3 \times 10^3}$$
• $$\large{\; 1 2 3, 0 0 0, 0 0 0 = 1 2 3 \times 10^6}$$
• $$\large{\; 1 2 3, 0 0 0, 0 0 0 = .1 2 3 \times 10^9}$$
• Equation  -  A statement containing one or more variables that are either added, subtracted, divided or multiplied to get an answer.  $$\large{ 13a^2+7x-21=19 }$$
• Elementary Arithmetic  -  Includes the simplified operations of addition, subtraction, division, and multiplication.
• Exponent (Index, Power)  -  Is how many times you multiply the number.  Term is $$\large{ 13a^2 }$$, the exponent is $$\large{ 2 }$$ .
• Expression  -  A group of terms, coefficients, constants and variables separate by an operation.  An equation  $$\large{13a^2+7x-21=19 }$$ , the expressions is  $$\large{ 13a^2+7x-21 }$$  and  $$\large{ 19 }$$.

### F

• Factor Number  -  Numbers $$\large{ 3 }$$ and $$\large{ 8 }$$ are factors that can be multiplied to get another number $$\large{ 24 }$$ .  Equation $$\large{ 3 \times 8=24 }$$
• Factoring  -  Factor $$\large{ 7 \left(x-3\right) }$$ expand to  $$\large{ 7x-21 }$$  or expressed as  $$\large{ 7 \left(x-3\right) = 7x-21 }$$ .
• Factorial  -  The symbol is  $$\large{ ! }$$ .  Multiply all whole numbers from the chosen number down to 1.  $$\large{ 5!=5\cdot 4\cdot 3\cdot 2\cdot 1=120 }$$  or  $$\large{ n!=\left(n+3\right) 2y\cdot 2\cdot 1=n }$$
• Formula  -  An expression in symbols used to calculate a desired result in mathematics and chemistry.
• Fractional Exponent  -  Is how mant times you multiply the number.  Term is $$\large{ 13a^{ \frac{2}{3} } }$$, the exponent is $$\large{ \frac{2}{3} }$$ .
• Fraction  -  A part  $$\large{ \frac{3}{8} }$$  of the whole.
• Adding Fractions  -  $$\large{ \frac{a}{b}\;+\;\frac{c}{d} = \frac{ \left( a\;d \right) \;+\; \left( b\;c \right) }{b\;d} }$$
• Subtract Fractions  -  $$\large{ \frac{a}{b}\;-\;\frac{c}{d} = \frac{ \left( a\;d \right) \;-\; \left( b\;c \right) }{b\;d} }$$
• Multiply Fractions  -  $$\large{ \frac{a}{b}\;\frac{c}{d} = \frac{a\;c}{b\;d} }$$
• Divide Fractions  -  $$\large{ \frac{a}{b}\;\div\;\frac{c}{d} = \frac{ a\;d }{b\;c} }$$
• Function  -  A relationship where a set of inputs (domain) determine a set of possible outputs (range).  The function of  $$\large{ f \left( x \right) = 5\;x }$$  is  $$\large{ f \left( x \right) }$$ , the function name is  $$\large{ f }$$ , the input value is  $$\large{ \left( x \right) }$$ , and the output is (what the function does) $$\large{ 5\;x }$$ .

### G

• Geometric Mean  -  Two  numbers  $$\large{ a }$$  and  $$\large{ b }$$  is the number  $$\large{ c }$$  whose square equals the product  $$\large{ c^2 = a\;b }$$ .
• Geometric Sequence (Geometric Progression)  -  Multipling the previous term by a constant.  $$\large{ 2 }$$  the sequence   $$\large{ 1, 2, 4, 8, 16, 32, ... }$$  or  $$\large{ b }$$  the sequence  $$\large{ a, ab, ab^2, ab^3, ... }$$
• Geometric Series  -  A series of the terms of a geometric sequence that has a constanr ratio.  $$\large{ 1 + 2 + 4 + 8 + 16 + 32 \;+ ... }$$
• Greatest Commom Factor  -  The highest number that divides exactly into two or more numbers.  factors of $$\large{12}$$ are $$\large{ 1, 2, 3, 4, 6,12 }$$ and factors of $$\large{16}$$ are $$\large{ 1, 2, 4, 8, 16 }$$, the greatest common factor of $$\large{12}$$ and $$\large{16}$$ is $$\large{4}$$

### H

• Hexadecimal Number  -  Based on the number 16.  $$\large{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F }$$

### I

• Imaginary Number  -  A number  $$\large{ i }$$  (imaginary symbol) when squared gives a negative number  $$\large{ i^2 = -1}$$  or  $$\large{\sqrt{-1} = i }$$ .
• Real  $$\large{ -2^2=4 }$$    Imaginary  $$\large{ 2i^2=-4 }$$
• Improper Fraction  -  A fraction  $$\large{ \frac{21}{7} }$$  that has a larger numerator than denominator.
• Integer Number  -  A whole numbers that can be either positive or negative  $$\large{ ... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }$$  with no fractions.
• Inverse (Reciprocal)  -  Reverses the effect of another number.  $$\large{ 3\cdot 7 = 21 }$$  inverse is  $$\large{ \frac{21}{7} = 3 }$$ ,  $$\large{ 19 }$$  inverse is  $$\large{ -19 }$$ .
• Irrational Number  -  A number that cannot be written as a fraction.  $$\large{ \sqrt{2} }$$ ,  $$\large{ \pi=3.1415926535 ... }$$ ,  $$\large{ e=2.71828182... }$$

J

K

### L

• Like Terms  -  These are terms where the variables are the same.  The terms are  $$\large{ 13a^2, 3a^2, -3a^2 }$$, the like terms are $$\large{ a^2 }$$  or the terms are  $$\large{ 13a^2 + 3a^2 + -3a^2 }$$ , the like terms are  $$\large{ a^2 }$$
• Line  -  A straight path between two points or multiple points.
• Linear  -  In a straight line.

### M

• Matrix  -  A rectangular or square array of numbers using either brackets  $$\large{ [\;] }$$  or parentheses  $$\large{ (\;) }$$ .                   $${ \begin{bmatrix} 4 & 7 & 2.54 \\ -9 & 3.1 & 3 \\ 13 & 1.2 & -9 \end{bmatrix} }$$   or   $${ \begin{pmatrix} 4 & 7 & 2.54 \\ -9 & 3.1 & 3 & \\ 13 & 1.2 & -9 \end{pmatrix} }$$
• Mean  -  The sum of all numbers in a set divided by the number of the values.  $$\large{ (2 + 3 + 4 + 5) / 4 = 3.5 }$$
• Mathematical Operation  -  addition $$\;(+),\;$$ subtraction $$\;(-),\;$$ multiplication $$\;(\times),\;$$ division $$\;(+)\;$$
• Minuend  -  The first number in a set of terms  $$\large{ 3 - 7 = - 4 }$$  to be subtracted.  $$\large{ 3 }$$  is the minuend,  $$\large{ 7 }$$  is the subtrahend, and  $$\large{ -4 }$$  is the difference.
• Mixed Number  -  A number written as  $$\large{13 \frac{3}{8} }$$  a whole number  $$\large{13 }$$ and a fraction  $$\large{ \frac{3}{8} }$$ .
• Monomial  -  A polynomial with only one term  $$\large{ 13a^2 }$$ .
• Mutually Exclusive (Disjoint Event)  -  Events that have no outcomes in common.
• Multiplicand  -  In a set of terms  $$\large{ 3 \times 7 = 21 }$$  the number that is multiplied.  $$\large{ 7 }$$  is the multiplicand,  $$\large{ 3 }$$  is the multiplier, and  $$\large{ 21 }$$  is the product.
• Multiplier  -  In a set of terms  $$\large{ 3 \times 7 = 21 }$$  the number that you are multiplying by.  $$\large{ 3 }$$  is the multiplier,  $$\large{ 7 }$$  is the multiplicand, and  $$\large{ 21 }$$  is the product.

### N

• Natural number  -  Can be either counting numbers  $$\large{ 1, 2, 3, 4, 5, 6, ... }$$  or whole numbers  $$\large{ 0, 1, 2, 3, 4, 5, 6, ... }$$ .
• Negative Exponent  -  Is how mant times you multiply the number.  Term is $$\large{ 13^{-2} = \frac{1}{13^2} = \frac{1}{169} }$$, the exponent is $$\large{ -2 }$$
• Negative Number  -  It is the oposite of a whole number  $$\large{ ... , -5, -4, -3, -2, -1 }$$  or decimal number excluding  $$\large{ 0 }$$ .
• nth Root  -  Some number  $$\large{ n }$$  used as  $$\large{ ^n\sqrt{a} }$$.
• Number  -  A mathmatical object used to count.
• Number Line  -  Every point on a line represents a real number.
• Number Sentence  -  An equation of numbers and operations that expresses the relationship between them.  $$\large{ 3 + 7 = 10 \;,\; 3 < 7 }$$
• Number Properties  -  Associative, communitive, and distributive
• Number Types  - digits, fractional number, integer number, irrational number, natural number, numeral, rational number, real number, transcendental number, and whole number
• Numeral  -  A single symbol to make a numeral like  $$\large{ 2119 }$$ .
• Numerator  -  The number of parts is  $$\large{ 3 }$$, fraction is  $$\large{ \frac{3}{8} }$$ .

### O

• Octal Number  -  A number system based on 8  $$\large{ 0, 1, 2, 3, 4, 5, 6, 7 }$$
• Operator  -  A symbol such as  $$\large{ +, -, ... }$$
• Order of Operation  -  Parenthese (inside), exponents, multiplication and division (left to right), addition and subtraction (left to right)
• Ordered Pair  -  Two numbers  $$\large{ \left(7, 21\right) }$$  or  $$\large{ \left(x, y\right) }$$  written in a certain order.
• Ordered Triple  -  Three numbers  $$\large{ \left(7, 21, 19\right) }$$  or  $$\large{ \left(x, y, z\right) }$$  written in a certain order.
• Ordered n  -  Multiple numbers  $$\large{ \left(7, 14, 21, ..., x_n\right) }$$  or  $$\large{ \left(x_1, x_2, x_3, ...,x_n\right) }$$  written in a certain order.

### P

• Partial Fraction  -  A fraction  $$\large{\frac{3a^2-7x}{13a^2+7x-21} }$$  that is broken into one or more smaller parts $$\large{\frac{a}{7x} + \frac{9}{4+x} }$$ .
• Perfect Number  -  A whole number that is equal to the sum of its positive factors except the number itself.  $$\large{1+2+4+7=14}$$ ,  $$\large{14}$$ is a perfect number because the positive factors are  $$\large{1, 2, 4, 7,14}$$ .
• Permutation  -  A set of objects in which the order is important.  $$\large{ \left(7, 21, 19\right) }$$
• Polynomial  -  The sum of two or more terms.  A term can have constants, exponents and variables, such as  $$\large{ 13a^2 }$$ .  Put them together and you get a polynomial.
• Monomial  -  1 term  $$\large{ 13a^2 }$$
• Binomial  -  2 terms  $$\large{ 13a^2+7x }$$
• Trinomial  -  3 terms  $$\large{ 13a^2+7x-21 }$$
• Porportional  -  When the ratio of two variables are constant.
• Positive Number  -  A counting number  $$\large{ 1, 2, 3, 4, 5, 6,... }$$  or decimal number excluding  $$\large{ 0 }$$ .
• Postulate  -  A statement that is assumed true without proof.
• Let $$\large{\;a}$$ , $$\large{b}$$ and $$\large{c}$$ be real numbers.
• Reflexive Property  -  $$\large{a = a\; }$$ (A quantity is congruent (equal) to itself.)
• Symmetric Property  -  If $$\large{\;a = b\; }$$, then $$\large{\;b = a }$$
• Transitive Property  -  If $$\large{\;a = b\; }$$ and $$\large{\;b = c\; }$$ , then $$\large{\;a = c }$$
• Addition Postulate  -  If $$\large{\;a = b\; }$$ , then $$\large{\;a + c = b + c\; }$$
• Subtraction Postulate  -  If $$\large{\;a = b\; }$$ , then $$\large{\;a - c = b - c\; }$$
• Multiplication Postulate  -  If $$\large{\;a = b\; }$$ , then $$\large{\;ac = bc\; }$$
• Division Postulate  -  If $$\large{\;a = b\; }$$ and $$\large{\;c \ne 0\; }$$ , then $$\large{\; \frac {a}{c} = \frac {b}{c}\; }$$
• Substitution Postulate  -  If $$\large{\;a = b\; }$$ , then $$\large{\;a\; }$$ can be substituted for $$\large{\;b\; }$$ in any expression.
• Distributive Postulate  -  $$\large{\;a \left (b + c \right ) = ab + ac\; }$$
• A straight line contains at least two points.
• If two lines intersect, the intersection is only one point.
• If two planes intersect, the intersection is only one line.
• A plane must contain at least three noncollinear points.
• Power (Exponent, Index)  -  Is how mant times you multiply the number.  Term is $$\large{ 13a^2 }$$, the exponent is $$\large{ 2 }$$ .
• Prime Factor  -  A factor  $$\large{13, 7 }$$  are prime numbers.  $$\large{13\cdot 7 =91 }$$
• Prime Number  -  A number that can be divided evenly only by  $$\large{1}$$ , or itself and it must be a whole number greater than $$\large{1}$$ .
• Product  -  In a set of terms  $$\large{ 3 \times 7 = 21 }$$  the multiplied answer.  $$\large{ 21 }$$  is the product,  $$\large{ 3 }$$  is the multiplier, and  $$\large{ 7 }$$  is the multiplicand.
• Proper Factor  -  Any of the factors of a number, except $$\large{1}$$ or the number itself.
• Proper Fraction  -  When the numerator  $$\large{ 3 }$$  is less than the demominator  $$\large{ 8 }$$  of a fraction like  $$\large{ \frac{3}{8} }$$ .

### Q

• Quartile  -  One of three values that divide a data set into four equal sections.   $$\large{ 2, 4, 4, 5, 6, 7, 8 }$$ , the quartiles are  $$\large{ 4 }$$ (lower quartile), $$\large{ 5 }$$ (middle quartile), and $$\large{ 7 }$$ (upper quartile).
• Quotient  -  In a set of terms  $$\large{ 3 \div 7 = 0.43 }$$  the answer.  $$\large{ 0.43 }$$  is the quotient,  $$\large{ 3 }$$  is the dividend, and  $$\large{ 7 }$$  is the divisor.

### R

• Radical  -  An expression  $$\large{ 13a^2+7x-23 }$$  that is a root  $$\large{ \sqrt{13a^2+7x-23} }$$ .  The length of the bar  $$\large{ \sqrt{13a^2}+7x-23 }$$  tells how much of the expression is used.
• Radicand  -  The number under the symbol $$\large{ \sqrt{x} }$$
• Rational Number  -  Any number that can be expressed as a ratio (fraction) of two integers numbers.  $$\large{ 0=\frac{0}{1} }$$ ,  $$\large{ 0.125=\frac{1}{8} }$$ , $$\large{ 1.5=\frac{3}{2} }$$
• Real Number  -  Any number  $$\large{3, \frac{3}{4}, 13.45, -3.56, ... }$$  that is normally used.
• Reciprocal (Inverse)  -  Reverses the effect of another number.  $$\large{ 3\cdot 7 = 21 }$$  inverse is  $$\large{ \frac{21}{7} = 3 }$$ ,  $$\large{ 19 }$$  inverse is  $$\large{ -19 }$$ .
• Remainder  -  What is left over after long division.  $$\large{ 7 \; / \;13 = 1 }$$  r $$\large{ 6 }$$
• Repeating Decimal  -  A decimal that keeps recurring over and over.  $$\large{ 0.\overline{33} }$$
• Rounding  -  Replacing a number  $$\large{ 3.1415926535 ... }$$  with another number having less digits  $$\large{ 3.1415 }$$ .

### S

• Scalar Number  -  Any single real number  $$\large{3, \frac{3}{4}, 13.45, -3.56, ... }$$  used to measure.
• Scientific Notation  -  A way of writing large numbers  $$\large{ 1 2 3 4 5 6 7 8 . 9 }$$  into two part  $$\large{ 1 2 3 4 5 . 6 7 8 9 \;x\; 10^3 }$$ .
• Series  -  The sum of the terms of a sequence.  $$\large{ 1, 2, 3, 4, 5, 6, ... }$$ or $$\large{ 1 + 2 + 3 + ... +\; n }$$
• Set  -  A group of numbers, variables, or really anything written using $$\large{ (\; ) }$$ or $$\large{ [\; ] }$$ .
• Sequence  -  A sequence of numbers in an orderly list.
• $$\large{....,\; -15,\; -10,\; -5,\; 0,\; 5,\; 10,\; 15,\; ....}$$
• $$\large{....,\; 1,\; 7,\; 14,\; 21,\; 28,\; 35,\; ....}$$
• $$\large{....,\; -4.5,\; -3,\; -1.5,\; 0,\; 1.5,\; 3,\; 4.5,\; ....}$$
• Significant Digits  -  $$\large{ 1 2 3 0 }$$  Digits that are meaningful.  $$\large{ 0 . 0 1 2 3 0 }$$
• Square Number  -  $$\large{ 5 \cdot 5 = 25 }$$ ,  $$\large{ 25 }$$ is the square number.
• Square Root  -  $$\large{ \sqrt{25} = 5 }$$ ,  $$\large{ 5 }$$ is the square root.
• Subscript  -  A small letter or number lower than the normal text  $$\large{13_a^2 }$$ .
• Subset  -  A  $$\large{\left( 3, 4, 5 \right) }$$  is a subset of B  $$\large{\left( 1, 2, 3, 4, 5, 6, 7, 8, 9 \right) }$$ .
• Empty Set - $$\large{ (\; ) }$$  is a  subset of B
• Subtrahend  -  In a set of terms  $$\large{ 3 - 7 = - 4 }$$  the number to be subtracted.  $$\large{ 7 }$$  is the subtrahend, $$\large{ 3 }$$  is the minuend, and  $$\large{ -4 }$$  is the difference.
• Sum  -  In a set of terms  $$\large{ 3 + 7 = 10 }$$  it is the result.  $$\large{ 10 }$$ is the sum, and  $$\large{ 3 }$$  and  $$\large{ 7 }$$  are each addends.
• Superscript  -  A small letter or number higher than the normal text  $$\large{13_a^2 }$$ .
• Surd  -  A square root  $$\large{\sqrt{2} }$$  that can not be simplified by removing the square root $$\large{\sqrt{2} }$$ .  $$\large{\sqrt{4} }$$ can be simplified to $$\large{2 }$$ .
• Symmetry  -  Symmetry is when one shape becomes exactly like another if you flip or turn it.

### T

• Terms  -  Either a single number, a variable, or numbers and variables.  An equation  $$\large{13a^2+7x-21=19 }$$ , the terms are  $$\large{13a^2 }$$ , $$\large{7x }$$ , $$\large{21 }$$ , and  $$\large{19 }$$ .
• Theorem  -  A true statement that can be proven.
• Congruence of Segments
• Segment congruence is reflexive, symmetric, and transitive.
• Reflexive - For any segment $$\;AB\;$$, $$\;AB\;$$AB is congruent to $$\;AB\;$$
• Symmetric - If $$\;AB = CD\;$$ , then $$\;CD = AB\;$$
• Transitive - If $$\;AB = CD\;$$ and $$\;CD = EF\;$$ . then $$\;AB = EF\;$$
• Congruent Angles
• Angle congruence is reflexive, symmetric, and transitive.
• Reflexive - For any $$\; \angle A\;$$, $$\; \angle A\; = \angle A$$
• Symmetric - If $$\; \angle A = \angle B \;$$ , then $$\; \angle B = \angle A \;$$
• Transitive - If $$\; \angle A = \angle B \;$$ and $$\; \angle B = \angle C \;$$, then $$\; \angle A = \angle C \;$$
• Right Angle Congruence
• All right angles are congruent.
• Congruent Supplements
• If two angles are supplementary to the same angle, then they are congruent.
• If two angles are supplementary to congruent angles, then they are congruent.
• Congruent Complementary
• If two angles are complementary to the same angle, then they are congruent.
• If two angles are complementary to congruent angles, then they are congruent.
• Vertical Angles Congruence
• Vertical angles are always congruent.
• Transcendental Number  -  A real number that cannot be the root of a polynomial equation with rational coefficients.  pi, e, Euler's constant, Catalan's constant, Liouville's number, Chaitin's constant, Chapernowne's number, Morse-Thue's number, Feigenbaum number
• Triangular Number  -  A number that can make a triangular dot pattern.  Each side in the triangle containes the same number of dots.  1 = 1 dot, 2 = 3 dots, 3 = 6 dots, 4 = 10 dots, 5 = 15 dots, etc.
• Trinomial  -  A polynomial with only three term  $$\large{ 13a^2+7x-21 }$$ .

U

### V

• Variable  -  Letters or symbols that are used to represent unknown values that can change depending in the infomation.  An equation  $$\large{13a^2+7x-21=19 }$$ , the variables are  $$\large{a, x }$$ .
• Vinculum  -  A line that is part of an expresson  $$\large{ \sqrt{a+b} }$$  or  $$\large{ \frac{a+b}{a-b} }$$  to show everything above or below the line is one group.

### W

• Whole Number  -  Just positive numbers  $$\large{ 0, 1, 2, 3, 4, 5, 6, ... }$$  with no fractions.

X

Y

### Z

• Zero  -  A whole number that is neither  $$\large{ - }$$  or  $$\large{ + }$$  and contains no value.

Display #
Title
Commutative Property
Congruence of Segments
Congruent Angles
Congruent Complementary
Congruent Right Angle

Tags: Glossaries