is the following correct to the question,

the negation should be there are no smallest numbers in every non-epmty subset of the natural numbers, but I am ot sure how to put this in symbol form?

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- October 22nd 2013, 01:55 PMTweetynegation of a statement and quantifiers,
is the following correct to the question,

the negation should be there are no smallest numbers in every non-epmty subset of the natural numbers, but I am ot sure how to put this in symbol form? - October 22nd 2013, 02:15 PMemakarovRe: negation of a statement and quantifiers,
The phrase "There are no smallest numbers in every subset", unfortunately, is ambiguous in English. I hate when people say, "Every group of people does not have a leader" when they mean "

*Not*every group of people has a leader". So, if by "Every subset does not have the smallest element" you mean what this phrase should mean, i.e., that there is not a single subset that has the smallest element, then this is*not*the negation of "Every subset has the smallest element".

The problem directs you to first write the original statement in quantifiers. Then negating it would be easy. - October 22nd 2013, 02:18 PMHallsofIvyRe: negation of a statement and quantifiers,
Well, your first problem is that "there are no smallest numbers in every non-empty subset of the natural numbers" is not correct. The negation of "for all" or "every" is "there exist". The negation of "every non-empty set of natural numbers contains a smallest number" is "there

**exist**a non-empty set of natural numbers that does not contain a smallest number".