Quantifiers - does this order matter?

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SUMMARY

The discussion clarifies that the order of quantifiers in mathematical logic does not affect the meaning when using existential quantifiers. Specifically, the expressions \exists x, \exists y and \exists y, \exists x are equivalent. This conclusion contrasts with the interpretation of a professor who believes the order is significant, suggesting a misunderstanding of the principles of quantification in logic. The community consensus confirms that both expressions convey the same existential relationship.

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Is saying [itex]\exists[/itex]x, [itex]\exists[/itex]y
the same as saying [itex]\exists[/itex]y, [itex]\exists[/itex]x?
 
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Hi gmmstr827! :smile:

No, in this case, the order doesn't matter.
 
Alright, because the professor I have right now thinks those are two completely different things. He reads it as "there exists an x such that there exists a y (for that specific x)." This is the second time I had the class (it didn't transfer colleges) and my previous professor said they're the same thing.

Is there a law describing this somewhere?
 

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