# for all quantifier

• Jul 26th 2011, 08:57 AM
Tina
for all quantifier
Hello

A is a formula with variables x and y. What is the difference between

$\displaystyle \forall$ (x,y) A

$\displaystyle \forall$(x)$\displaystyle \forall$(y)A

Thank you...
• Jul 26th 2011, 09:23 AM
MoeBlee
Re: for all quantifier
Unless there's some special context in mind, I'd take them both as the same.

[Here using 'A' for the quantifier in ASCII:]

AxAyP

AxyP

some people write

(x)(y)P

They all mean the same.
• Jul 26th 2011, 09:24 AM
TheChaz
Re: for all quantifier
What makes you think that there is a difference?
Can you come up with any examples where they wouldn't be the same?
• Jul 26th 2011, 09:42 AM
FernandoRevilla
Re: for all quantifier
If $\displaystyle \mathcal{L}$ is a first order language with variable letters $\displaystyle x,y,\ldots$ then, $\displaystyle (\forall x)(\forall y)A$ is a well formed formula and $\displaystyle (\forall (x,y))A$ it is not. We can of course use $\displaystyle (\forall (x,y))A$ as an alternative notation for $\displaystyle (\forall x)(\forall y)A$ .
• Jul 26th 2011, 09:47 AM
MoeBlee
Re: for all quantifier
I'd rather avoid the clutter of parenethess. It's enough to have

AxAyP

And then to allow that to be indicated by

AxyP
• Jul 28th 2011, 06:23 PM
Tina
Re: for all quantifier
Thank you all for your replies .