Question

Can you explain Inverse Axiom (Both addition and multiplication)?

Can anyone explain this in a "PROOFING" manner?
... (see below)

Answer 1

Is this true? Explain why.
\[4(\frac{ 1 }{ 4 }) = 1\]

Answer 2

Do you know what multiplication inverse is?

Answer 3

reciprocal

Answer 4

A number multiplied by its reciprocal is always equal to 1.

Answer 5

"A number which is, 4, multiplied by its reciprocal, 1/4, is equal to 1." Is that how your write in proofing?

Answer 6

\[a \cdot a^{-1}=1 \text{ for all } a \neq 0\]
This is just the multiplicative inverse property

Answer 7

Ok so what axiom system your working on ??

Answer 8

I'm working on all types of axiom. From the 5 basics of axiom of equality to the other axioms. I'm just wondering on how could explain it. I saw this material in the internet: http://www.mathhands.com/046/hw/046c01s06ns.pdf Under the "Some questions to think about". Do you have any idea how to explain it in a way the author wants it to be?

Answer 9

In addition to that question, I can't seem to find any other explanation or differences between the 5 basic axioms of Algebra ( Reflexive, Symmetric, Transitive, Additive, and Multiplicative.

Answer 10

so I guess you are looking for something more then "example: 1/3 is the multiplicative inverse of 3 so 1/3*3=1 or 3*1/3=1" ?

Answer 11

So if the Prof asked me, "True, False, WDKY (we don’t know yet))
\[3(\frac{ 1 }{ 3 }) =3\]
Do you know why? exp
lain."

How will I form my answer?

Answer 12

@freckles

Answer 13

that would be false
because 3*1/3=1

Answer 14

we already mentioned the multiplicative inverse property above
\[a \neq 0\]
\[a (\frac{1}{a})=1 \text{ since } a \text{ and } \frac{1}{a} \text{ are multplicative inverses of each other }\]

Answer 15

I don't know what other answer you are looking for honestly

Answer 16

Maybe, I was expecting a complicated explanation. T.T If it's that simple, then okay. Thank you very much.