Math & Infinity: Zero vs. Infinity Problem

[CozmicScott]

Are zero and infinity the biggest problems for math? Can they ever be the same. zero is infinitly nothing, and infinty stops zero times?

 

[Hurkyl]

The only problem math has with zero and infinity is that people love to insist that they're mysterious, and in doing so, prevent themselves from actually learning about it.

 

[CRGreathouse]

Infinity, like real numbers, is a simplification that let's us do work more easily. Consider the "infinity" setting on the zoom of a camera: it's not that they expect you to take pictures of objects infinitely distant, but that a true infinite setting is good enough for objects really far away, like a thousand feet. For a camera, 1000 feet is close to infinity, while 1 foot is far from 10 feet.

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.

 

[CozmicScott]

they r mysterious and, when math is done, and they have been thrown out or disregarded to simpilfy things i think it cheats the equations truths somewhat. Sorry I'm a real novice at these discussions , and maybe I don't express what I mean well , but that's why I'm here too gain a better understanding. Sorry if I sound stupid, and make it too mysterious, but these little things bother me. zero + infinity.

 

[symbolipoint]

Zero is a specific number, and infinitely is not a number. Infinitely is what... unboundedness of value?

 

[Hurkyl]

There is not an integer named infinity.
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'.

 

[uman]

Note also that "0 + infinity" has no meaning in the real numbers. In the *extended* real number system, in which "infinity" and "-infinity" exist, 0 + infinity = infinity

 

[schroder]

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!

 

[Hurkyl]

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!

Bad advice. How long is the real line?

Answers should always be checked, no matter what the answer is.

 

[schroder]

Answers should always be 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?

 

[Dragonfall]

Bad advice. How long is the real line?

0.208780721 furlong

 

[disregardthat]

0.208780721 furlong

i c wat u did ther, vry clvr

 

[Tac-Tics]

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.