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Level 41

Classification of Numbers


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Natural numbers
A group of numbers that include 1,2, 3,.....
0,1,2,3,4,5...
Whole Numbers
Integers
the set of positive whole numbers and their opposites(negative numbers) and 0
Rational numbers
Numbers that include integers, wholes, and natural numbers.
Irrational Numbers
any number that cannot be expressed as a fraction.
real numbers
Any Number
1,2,3,4...
counting (natural)
no pattern
Irrational numbers
0!!!,1,2,3,4...
Whole numbers
Substitution property
a(b) = (ab)
1/-a = -1/a
Property of reciprocals of the opposite of a number
commutative property of addition
If the order of the terms changes, the sum stays the same.
ab=ba
Commutative Property of Multiplication
associative property of addition
When the grouping of terms changes, the sum stays the same.
(a∙b)c = a (b∙c)
Associative property of multiplication
a (-1) = -a
Multiplicative property of -1
a∙1 = a
Identity Property of Multiplication
a∙ ¹⁄a = 1
Property of Reciprocals (Inverse property of Multiplication)
a∙0 = 0
Multiplicative property of zero
a + (-a) = 0
Property of Opposites (Inverse property of addition)
Definition of Division
a ⁄ c + b ⁄ c = a+b ⁄ c or a ⁄ c - b ⁄ c = a-b ⁄ c
-(X+Y) = (-X) + (-Y)
Property of the opposite of a sum
Definition of Substraction
a + (-b) = a-b
a=a, x+3=x+3
Property of Equality-Reflexive
Property of Equality-Symmetric
If a=b then b=a if x=3 then 3=x
Property of Equality-Transitive
If a=b and b=c then a=c
Real Number (R)
Any type of number
Rational Number (Q)
Can be expressed as a ratio; terminating decimal, or repeating decimal.
Irrational Number (I)
Is a non terminating decimal, or does not repeat; 3.14 or a square root that cant be squared.
Integers (Z)
Any positive or negative number (as long as it isn't a decimal)
Natural Number (N)
Starting from 1, and increasing by 1; 1,2,3,4,5...... (negatives or 0 is not included)
Whole Numbers (W)
Includes all natural numbers AND 0
Commutative
Changing the order of the factors does not change the product.
associative
Changing the grouping of the factors does not change the product.
Identity
The product of any number and one is that number.
Inverse
a + (-a) = 0 = (-a) + a OR a * 1/a = 1 = 1/a * a; a cant be 0
Closure
(a + b) and (a * b) is a real number
Distributive
This is done by breaking a large fact into two smaller known facts.
Prime number
A number that can only be divided by 1 and itself. The numbers left at the bottom of the tree
Composite number
a number with more than two factors.
sum
the answer to an addition problem
difference
the answer to a subtraction problem
product
the answer to a multiplication problem
quotient
the answer to a division problem
Whole Numbers
Zero and the counting numbers 1, 2, 3, 4, 5, 6, and so on. If a number has a negative sign, a decimal point, or a part that's a fraction, it is NOT a whole number.
Imaginary numbers
A subset of the complex number system. A number which can be written in the form a + bi where b ≠ 0 and i represents the square root of -1.
Consecutive integers
Integers that follow each other in order with a difference of 1 between every two numbers. Ex. 7, 8, 9. Represented by n, n+1, n+2, n + 3 ...
Reflexive Property of Equality
Any number equals itself. x = x
Symmetric Property of Equality
For all real numbers x and y, if x = y, then y = x.
Transitive Property of Equality
For all real numbers x, y, and z , if x = y and y = z, then x = z.
Addition Property of Equality
For all real numbers x, y, and z, if x = y, then x + z = y + z.
Subtraction Property of Equality
For all real numbers x, y, and z, if x = y, then x - z = y - z.
Multiplication Property of Equality
For all real numbers x, y, and z, if x = y, then xz = yz.
Division Property of Equality
For all real numbers x, y, and z, if x = y, and z ≠ 0, then x/z = y/z. You can divide each side of an equation by the same non-zero number and not change its truth value.
Substitution Property of Equality
For all real numbers x and y, if x = y , then y can be substituted for x in any expression and vice versa.
Distributive Property of Equality
For all real numbers x, y, and z, x(y + z) = xy + xz.