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soopo
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Homework Statement
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
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"?