## Disprove the nested quantifier

I have trouble disproving the following expression

I worded it as follows:

The product of certain number and every other nonzero number is 1
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 First of all, does the problem specify what the domain is for x and y? To start, lets back things up a bit. In mathematical terms, the statement is as follows: There exists an x for every possible y value, such that if y isn't zero, when you choose an x-value, you can multiply it by every y-value in the domain, and the result is 1. So, assuming the domain is real numbers, for both x and y, lets try choosing a value for x: Let x = 5. What value of y would make the statement true? y = 1/5. So, we've tested JUST ONE y-value. x = 5 has to work for EVERY single y. Can you think of a y-value that would make the statement false? EDIT: If anyone thinks my reply contains fallacious ideas, please inform me.