Prove the function f:Z x Z → Z given by f(m,n) = 2m - n is Onto(Surjective)

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Prove the function f:Z x Z → Z given by f(m,n) = 2m - n is Onto(Surjective)

[@SchmidtKaiser97]

why does the pairing (0,-y) work to prove the whole function is onto? what if m is not equal to 0? How does one pairing prove for all pairings?

[@tsoeng]

Hey check this answer: math.stackexchange.com/questions/3329542/determine-if-f-z-%c3%97-z-%e2%86%92-z-is-onto

[@Gargantupimp]

The existential quantifier. You only have to prove that there exists AT LEAST ONE case in which the function parameters equal y (the codomain). (0, -y) is just one case which proves this. I did it with (y, y) which works as well.

[@FinnishArmy]

This made absolutely zero sense to me.

[@TheMathSorcerer]

LOL I am sorry:)

[@FinnishArmy]

@@TheMathSorcerer I have got a Discrete Math exam tomorrow and more than half the class doesn't understand anything.

[@denizdemir9255]

@@FinnishArmy 9 months later and I agree broski.

[@somilarora4130]

same the textbook questions are very different from textbook examples

[@Nandinandito]

I mean, I can understand that it works, but I don't understand when it wouldn't work.

[@tsoeng]

Hey, check this answer - math.stackexchange.com/questions/3329542/determine-if-f-z-%c3%97-z-%e2%86%92-z-is-onto

[@NotJoSa]

DUDE AFTER USING SLADER AND WATCHING THIS VIDEO I FANNYLLYLLY UNDERSTOOD IT

[@eswyatt]

Someday pizza delivery will be surjective; it will just appear in my stomach. Until then, I'll have to keep looking for it in the shrubs.

[@albertlewis332]

You are life saver. Thank you for all you do!!

[@TheMathSorcerer]

np!!

[@123blalala]

Helped me a lot thank you !

[@TheMathSorcerer]

awesome!

[@manyabhutani8235]

is this injective too????

[@Jose-pf7id]

Thank you!

[@yosufgaper6853]

thank you do much "tears" ❤️

[@himanshinirwan9563]

please do it for f:N×N->N

[@shaolintexchrislightninga.8234]

Action Bronson°°

[@mjstc4776]

Amazing videos, thank you!

[@irenalena1167]

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[@irenalena1167]

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[@irenalena1167]

Rest

[@irenalena1167]

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[@jaamalarane959]

you are using a counterexample to proof which is not correct

[@TheMathSorcerer]

just checked, everything looks ok here:)

[@mohitpatel7522]

binod video

[@WillCastle]

Can you explain what ZxZ means

[@ahsanraza135]

Is f(m,n)=|n| onto?

[@Puja4550]

How can we check that if this function is one one or not?

[@goplay5936]

Can u tell me how to check whether f(m,n) = |m| - |n| is onto or not?

[@elicgoik]

this is what im trying to figure out

[@moski9861]

It is not onto because m and n are absolute value which are just simple positive numbers.

[@phinkurniawan2793]

i still coonfuse if (m,n) the codomain is Z x Z and domain which is y is Z if i take 2 then m can be 0 but how n become -2 but there is no Z x Z = -2 or maybe 2

[@phinkurniawan2793]

Z is any number that is integer right?