Verification Procedures for Modified Numeral Quantifiers Form

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mathematicians really like being lazy if they can get away with it and one of the ways that we allow ourselves to be lazy or perhaps efficient is the better word is to come up with new terminology new symbols that allow us to collapse larger more cumbersome things into shorthand and so when we have some large amount of mathematics where we're using the same sort of phrase over and over and over again we can just replace it by this one symbol so that's what we're going to do with this universal quantifier it's like an upside down a and it means for all so just a little bit of shorthand now the reason why I care about this is let's go back to the idea of a predicate a predicate is something that is sometimes true or sometimes false but I might have it that the predicate is always true or it could be that for all values of X the predicate is true so this is why we call it a quantifier this for all quantify some properties about a predicate so the main use is in this form and the way I wri