Proof

[silent yoke]

I would like someone to look at my proof

Lemma:
If Integers N and S are both non-negative, then their product is also non negative

I will attempt to show that this statement is true via a proof by contradiction.

suppose that the product of 2 arbitrary non-negative integers N and S is a negative integer L

N and S are both non-negative integers which means their domain is of the natural numbers

N x S = L

N x S = S+S+S...+S The Definition for Multiplication for Natural Numbers

Since S and N are both Natural numbers, this means that no matter how little or many times we add it, it can't ever produce a negative number

[autumn wyvern]

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[abstract heron]

This is a direct proof, there is no need in your line of reasoning for the contradictory assumption

[silent yoke]

really ?

[abstract heron]

Also take another look at the last statement. “No matter how little or many times we add it” may be too vague

[abstract heron]

Yes, this is a common thing. We start out trying out a pbc, but along the way we find a much simpler direct proof

[silent yoke]

yeah i see it

[silent yoke]

this one i will try to fix

[abstract heron]

This is pretty much all that is needed

[silent yoke]

"Since S and N are both Natural numbers, this means that if we add S , N times or vice versa, it won't ever produce a negative number"

is this less vague ?

[abstract heron]

Yes

For the sake of practice, you may want to try using a more formal definition of addition on the natural numbers

[silent yoke]

okay

thank you

although this is my first time writing a proof

(kinda, this is the edited version after i got some feedback)

[silent yoke]

+close