Example
Using variables to stand for numbers, write an example of the following axiom:
Additive Inverse
a + (-a) = 0
3/4
-3/4
Give an example that shows:
Subtraction is NOT a commutative operation
5 - 7 = -2 and 7 - 5 = 2
Is the following set of numbers a field? If not, list the axiom or axioms that cause the axiom to be excluded:
{rational numbers}
It is a field
a letter that stand for an unspecified number
Using variables to stand for numbers, write an example of the following axiom:
Multiplicative Inverse
a * 1/a = 1
What is the multiplication inverse of 3/4
4/3
Give an example that shows:
{negative numbers} is NOT closed under multiplication
(-3) (-8) = 24
24 is not a negative number
Is the following set of numbers a field? If not, list the axiom or axioms that cause the axiom to be excluded:
{integers}
Not a field
the Multiplicative inverse of any integer would be a a fraction. A fraction is not an integer.
What is an expression
a collection of variables and constants connected by operation signs (+, -, *, /) which stands for a number
Using variables to stand for numbers, write an example of the following axiom:
Trichotomy
If x and y are real numbers, then one of the following is true,
y < x OR y > x OR y = x
What is the additive inverse of -4
4
Give an example that shows:
{digits} is NOT closed under addition
7 + 9 = 16
16 is not a digit, but a double digit number
Is the following set of numbers a field? If not, list the axiom or axioms that cause the axiom to be excluded:
{positive numbers}
Not a field
The additive inverse would be a negative number
The additive identity is zero, zero is not a positive number
What is an equation
Two expressions connected by an equal sign (=)
Using variables to stand for numbers, write an example of the following axiom:
Transitivity for Equality
If x = y and y = z, then x = z
What is the multiplicative inverse of -4
-1/4
Give an example that shows:
Subtraction is NOT an associative operation
10 - (3-2) = 9
(10-3) - 2 = 5
Is the following set of numbers a field? If not, list the axiom or axioms that cause the axiom to be excluded:
{non-negative numbers}
Not a field
The additive inverse would be a negative number
The additive identity would be zero, which is neither negative or non negative
Define Simplify
To put into simpler terms to make the expression easier to work with
Using variables to stand for numbers, write an example of the following axiom:
Transitivity for Order
If x > y and y > z, then x > z
What is the multiplicative inverse of
-5/6
-6/5
FREEBIE
FREEBIE
Is the following set of numbers a field? If not, list the axiom or axioms that cause the axiom to be excluded:
{odd numbers}
Not a field
The multiplicative inverse would be a fraction
Evenness and Oddness is only defined for integers
Finding a numerical solution to an equation