(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There exists y > 0 such that [[tex]y^{2} = x[/tex] if and only if [tex]x > 0[/tex]].

This means that "there is some positive number whose square equals all positive

numbers." - St. John College, Oxford

3. The attempt at a solution

I am not sure about this statement "- - some positive number whose square equals

all positive numbers", and particularly about the word "all".

I would read the statement as

If [tex] \exists y > 0[/tex], then [tex]\exists [ y^{2} = x[/tex] if and only if [tex]x > 0] [/tex]

It seems that the statement should be read as

If [tex] \exists y > 0[/tex], then [tex]\forall [ y^{2} = x[/tex] if and only if [tex]x > 0] [/tex]

Is there always "for all" after "such that"?

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# Homework Help: A Logic Problem

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