Why did the author introduce a new variable y in the proof?
According to what I read from the book, if x is a bounded variable and not stand for a particular object, then introducing a new variable is not needed.
#proof variable question
wind vine
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Why did the author introduce a new variable y in the proof?
According to what I ...
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Why did the author introduce a new variable y in the proof?
According to what I ...
can you link the of the book you're talking about ?
wind vine
velleman's "how to prove it"
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I skipped a word, but I meant the part where it says you don't need to introduce a new variable to prove forallx. P(x)
wind vine
I skipped a word, but I meant the part where it says you don't need to introduce...
I don't understand what you mean
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"According to what I read from the book, if x is a bounded variable and not stand for a particular object, then introducing a new variable is not needed."
could you show the exact statement from the book ? @wind vine
because to show (forall x, P(x)), you need to introduce a variable x and show that P(x) holds
wind vine
It's in the first paragraph in the second screen shot.
and I faced this again
This proof is to prove 2->3 (2. and 3. are in the screen shots)
this proof has y as a bounded variable on the first line, then let y be arbitrary later. I don't understand the differnce between this and the original proof.
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@wind vine these are not the same
on the first line, you are not proving forall, you are using it. Thus, they instantiate y with the variable x0, so that the body of the forall is true by replacing y with x0.
Later, they want to prove a forall, so they need to instantiate y and z and then prove the body of the forall with y and z.
wind vine
on the first line, you are not proving forall, you are using it. Thus, they inst...
In the first proof, the first line says let y be arbitrary, which I think is because there's already exists x (as a bounded variable) in givens, so the author replaces with y instead.
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yes, this may be the reason
wind vine
And in the second proof, when instantiating y and z, I think this is the same kind of situation but there's y as a bounded variable and y as a new variable.
wind vine
Isn't replacing y with a new variable needed as in the first proof?
wind vine
But as this says if x is a bounded variable, then no need to replace x
wind vine
And based on this if I say x is arbitrary instead of y is arbitrary in the first proof is also ok
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And based on this if I say x is arbitrary instead of y is arbitrary in the first...
yes
wind vine
yes
So it's ok to not use a new name as long as x is a bounded variable (which means x doesn't stand for a particular object)?
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exactly
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