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Disprove the nested quantifier 
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#1
Feb2013, 10:03 PM

P: 11

I have trouble disproving the following expression
I worded it as follows: The product of certain number and every other nonzero number is 1 


#2
Feb2113, 10:49 AM

P: 937

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 xvalue, you can multiply it by every yvalue 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 yvalue. x = 5 has to work for EVERY single y. Can you think of a yvalue that would make the statement false? EDIT: If anyone thinks my reply contains fallacious ideas, please inform me. 


#3
Feb2213, 08:56 AM

P: 937

@Albert, has my reply stirred any thoughts in your mind?



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