Quantifiers

Discrete Mathematics: Quantifiers
Topics discussed:
1) Definition of quantifiers.
2) Quantifiers in English with examples.
3) Types of quantifiers.
4) Examples of quantifiers.
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2:35 why not say for all numbers P(x) holds true(instead of +ve integers)?

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3:23
in the mathematical statement on the bottom right hand, shouldnt we specify that "for all x THAT ARE POSITIVE INTEGERS, p(x) is true"? (In line with the statement on the left, since we are focusing our attention on only positive integers, although i understand the unspoken fact that it would be true for negative integers as well)

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Bdw at 2:20 Its true for all real numbers not just positive ( [ -2+1 > -2] => [ -1 > -2 ] )

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In the example, you say that x+1 > x for all positive Integers but it is true for all Integers (positive & negative) I know you never explicitly say this isn't the case.

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4:40 or we can say there exist some positive integer such that Q(x) is true

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What if quantifier is not used in statement

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