>Employing strictly the properties of...

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>Employing strictly the properties of the set of rational numbers listed above

What did mean by this?

How does one go about proving i - iii employing strictly the properties of the set of rational numbers listed above?

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>>7806656

It might help if you post the properties that you cut off from the top of the page

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>>7806673

to do 1.(i):

ab+a(-b)

=a(b+(-b)) (by (v))

= a0 (by definition of additive inverses)

=a(0+0) (since 0 is additive inverse)

=a0+a0

in particular this implies a0=0 so a(-b)=-(ab)

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>>7806686

how do you prove the transposition part?

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>>7806727

What transposition are you referring to?

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>>7806730

ab+a(-b)

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>>7806744

I'm still not sure what you mean. ab+a(-b) is a number, not a transposition.

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>>7806750

I mean how did you get from a(-b)=-(ab) to ab + a(-b) = 0?

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>>7806757

-(ab) designates the additive inverse of ab, i.e. the unique number such that ab+(-ab)=0. So I showed ab+a(-b)=0, which implies a(-b)=-(ab).

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>>7806760

I get it now

cheers

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These are arithmetic axioms.

With these you can prove that

ab = 0 => that either a or b is 0

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>>7806656

> Question 3

Shouldn't it be for a != 0?

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