I'm grading homework right now and I'm honestly a bit

>>8457796
It's false, obviously.
What it is saying is essentially something like...
There exists a person X such that for all people Y, X is the mother of Y = there is one person who is everyone's mother.
This is clearly nonsense.
Also, for each = for all. Also, even if the quantifiers changed places it would still be false in the reals because negative numbers aren't squares.

What confuses me is how someone who does not understand basic logic is allowed to grade homework.

T

you need to add : or / to make sense of this.
∀y : ∃x / x= y^2

>>8457808
this

>>8457808
Let he who is without forgetfulness cast the first stone.

But thanks. I think you're probably right, but on your further note, if the quantifiers were to exchange places, I suspect it would be true, since for all y in the reals, there is some x such that x = y^2, yes?

Its "there exists an x so that for all y", if the quantors were switched it would be "for all x there exists y".

>>8457848
>Let he who is without forgetfulness cast the first stone.
You can frame it as a joke but I think he is completely right. Not only did you forget basic notation, you also seem to struggle with the elementary logic it is describing. How can you grade something without knowing the material yourself? Something is wrong.

>>8457866
Isn't that how it always is? Brainlets with initiative get the job while the socially crippled Assburgers stay on social support/their mom's basement.

>>8457871
No, it is not.

>>8457848
I literally addressed that case: if you switch the quantifiers, it is FALSE.
The statement: for all x, there exists a y such that x = y^2 is FALSE because there is no y in R such that y^2 = -1. The statement only holds over the nonnegative reals.

And yes, in logic, for each is equivalent to for all. There's a really easy proof of this: suppose the statement P holds for each x. Then it holds for all x. Suppose the statement P holds for all x. Then, it holds for x. But x was arbitrary, so it holds for each x.

And be careful of the quantifier shift fallacy as well: you cannot always shift quantifiers willy nilly, especially existential and universal quantifiers.

While it is true that for each person X, there exists a person Y such that Y is X's mother, it is NOT true that there exists an X for ALL Y such that X is Y's mother. Everyone has a mother, but there is no person who is everyone's mother!

>>8457871
Uh, not in the world of STEM, it isn't.

>>8457796
>I'm grading homework
>gets the question's answer wrong
You're fucking retarded. Are you a TA or something?