Infinite Plus One

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Around end of nineteenth and beginning of twentieth, Cantor foudn that infinite can be dealt with mathematically, and this forced a reconcenptualizition of what numbers are.

before this infinitie was s sort of vague idea. It was associated with god. The guy who invented infinite was jewish and was worried about treading into gods territory.

to be able to deal mathematically with inifinite, 'number' has to be very well defined. Necessiate inventing something more fundamental than numbers.

Whatis a number? Numbers can count how much of something, they can order things on a line, they can describe relative position. Infinite deal wtih this differently.

quanitity nubmers: set. a set of four objects can represent the number four. A set of four different objects is still four. we found that by matching each element in first set to the second. if they don't match, than there is a different number that the second set represents

infinite is a set with infinitely many objects. make a set out of the sets that represent the numbers we just found. a set that can't be matched to any finite number. its bigger than anything ocuntable.

infinite plus one. lets add an element to that set. then we will see how long it is. add zero to the front. compare to the first infinite to see which is the bigger set. well me can match them. for exvery number inthe first, there is one in the second.

so infinite plus one equals infinite

but later, there are other, biger infinites