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tsuomela : infinity   9

Number is Different from Quantity by Gregory Bateson
Number is different from quantity. This difference is basic for any sort of theorizing in behavioral science, any sort of imagining of what goes on between organisms or inside organisms as part of their processes of thought.

Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity there is no such jump, and because jump is missing in the world of quantity it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate.
by(GregoryBateson)  number  quantity  philosophy  infinity 
may 2009 by tsuomela
Good Math, Bad Math : Infinity is NOT a number
You can see the confusion right away: "1/0 is infinity because ...". Bzzt. No. 1/0 is not infinity. 1/0 is nothing. 1/0 isn't defined in our number systems: it's not a number. In fact, it's not just not a number, it's nothing. It's a meaningless expression. Asking what 1/0 is is like asking "What's the square root of a nice juicy plum?". Or what predicate makes the logical statement "∀x: P(x)∧¬P(x)" true?

If you treat infinity as a number, you fundamentally break everything that makes arithmetic work.
mathematics  infinity  number  definition  fields  peano-arithmetic 
october 2008 by tsuomela

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