Proofs with Scratch Work #1: "For all x, there exists y where xy^2 ≠ y - x" (ILIEKMATHPHYSICS)

This series mainly references "How to Prove It" by Daniel Velleman Third Edition. This type of exercise would be representative of one in Chapter 3.
In the "proofs with scratch work" videos, I use a random number generator to select problems (from this book), and do ones which I have not done yet. This video is an exercise from the book
Thanks and enjoy the video!

[@adw1z]

Doesn’t equal? I’m sorry I’m not sure if I am misunderstanding the question or it is just that easy:
if x =\= 0, choose y = 0
If x = 0, choose any y =\= 0

[@andyrendon-gi1fu]

I proved it by assuming that the negation of the statement is true and showing that we get a contradiction.
Assume the negation is true. Hence, for a particular x for which the statement is true we can choose y=0, since the statement is true for all y. Plugging these values in the equation will gives us that x must be zero.
However, if we choose instead y=1, then, being that x=0, we get 0=1. This is a contradiction.

[@skapun7744]

I loved this. Make more!

[@OtavioBraga-go9jy]

Finally, i found what i was looking for a playlist about Velleman's book. I'm reading it and, If you accept one suggestion for a future video, do The exercicie 17) 5.2 section(one to one and onto) from 2nd editor of How to prove it, i've tried the letter b),but i don't get anywhere. Thanks