Axioms of Equaltiy?

Question

Can someone please explain this as basic as it can be explained?

Opps, Equality....

Answer 1

An "axiom" is some statement that you assume is true, without proof. The axioms of equality can be written in different ways; here is one set:

The first axiom is called the reflexive axiom or the reflexive property. It states that any quantity is equal to itself. This is definitely one of the most obvious axioms there is.

The second axiom is the transitive axiom, or transitive property. If two quantities are both equal to a third quantity, then they are equal to each other.

The third axiom is the substitution axiom. If two quantities are equal, then one can be replaced by the other in any expression, and the result won't be changed.

The fourth axiom is called the partition axiom. A quantity is equal to the sum of its parts.

Then there are the arithmetic equality axioms. They basically say that if you have a true equation, then you can do the same arithmetic to each side and still have a true equation.

* Addition axiom: you can add the same thing to both sides. Thus, if a = b, then a + y = b + y.

* Subtraction axiom: you can subtract the same thing from both sides.

* Multiplication axiom: you can multiply both sides by the same thing.

* Division axiom: you can divide both sides by the same thing. (But be careful: you can't divide by zero.)

Answer 2

Additive axiom

if a, b and c are real numbers and a=b
then a+c=b+c.

ex
2=2
2+3=2+3 it is just adding the same quantity to both sides of the equation.

Multiplicative axiom

if a, b and c are real numbers and a=b
then ac=bc

ex
2=2
2 x 3= 2 x 3 it is just multiplying the same number to both sides of the equation.

Transitivity axiom

if a=b and b=c
then a=c

ex
jose's height= john's height
and john's height= james' height

therefore

jose's height=jame's height

Symmetric axiom

if a=b
then b=a it is just interchanging the expression

Reflexivity axiom

if a is a real number
then a=a

that is, any number is equal to itself

Answer 3

Axioms of Equality

Reflective

Trannsitive

Subtraction

Partition

Addition

Subtraction

Multiplication

Division

Click on the URL below for additional information concerning Axioms of Equality

www.sparknotes.com/math/geometry3/axiomsandpostulates/section1.html

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