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- Thread starter CozmicScott
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Hurkyl

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CRGreathouse

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Likewise, many problems are naturally integer problems, but we treat them as problems in the real numbers. What quantity maximizes profits, given a profit function pi? The true qualtity must be an integer, but for large numbers like a million units we treat the problem in real numbers rather than integers, just because it's easier to solve.

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symbolipoint

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Hurkyl

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There is not a rational number named infinity.

There is not a real number named infinity.

There is not a complex number named infinity.

There is a projective real number named (projective) infinity.

There is a projective complex number named (projective) infinity.

There are extended real numbers named positive infinity and negative infinity.

There is not a cardinal number named infinity.

There are many infinite cardinal numbers.

There is not an ordinal number named infinity.

There are many infinite ordinal numbers.

There is not a hyperreal number named infinity.

There are many infinite hyperreal numbers.

The infinite points of the projective plane are said to be 'at infinity'.

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And if you ever get “infinity” or “negative infinity” as an exact solution to a mathematical problem, it usually means you have done something wrong!

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Hurkyl

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Bad advice. :grumpy: How long is the real line?And if you ever get “infinity” or “negative infinity” as an exact solution to a mathematical problem, it usually means you have done something wrong!

Answers should

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Answers shouldalwaysbe checked, no matter what the answer is.

Yes! Particularly questions in Physics. An answer such as “infinite” energy should definitely cause a person to recheck his work. How much energy is “infinite” anyway? Enough for an infinite number of BB explosions in an infinite number of Universes over an infinite period of time! But a person can arrive at this “exact” answer by blindly following the mathematics. The relation GMm/r^2 simply means that the acceleration and force of gravity is inversely proportional to distance. But carried to the extreme, where r = 0; one can readily conclude that the acceleration and force go to infinity! But the acceleration of gravity at the center of the earth , or at the center of two superimposed particles, is exactly zero! The way to arrive at this is by reasoning, not blindly applying mathematics. Do you know why g is zero at the center of the earth, or at the center of two superpositioned particles?

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Bad advice. :grumpy: How long is the real line?

0.208780721 furlong

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disregardthat

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0.208780721 furlong

i c wat u did ther, vry clvr

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There is not an integer named infinity.

There is not a rational number named infinity.

There is not a real number named infinity.

...

A very nice list.

It should also be emphasized that math is about demonstrating truths in a FINITE number of steps. Can you add an infinite sequence together? No. Not literally. In most cases where you see an infinite sum or product or procedure of any sort, you are speaking about limits, not infinity.

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