Math & Infinity: Zero vs. Infinity Problem

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In summary, the conversation discusses the misconceptions and misunderstandings surrounding the concepts of zero and infinity in math. It is explained that these concepts are not mysterious, but are simply simplifications that allow for easier problem-solving. The conversation also mentions that the use of infinity or negative infinity as an exact solution in math is usually a sign that there is a mistake in the calculations. Additionally, it is emphasized that math is about demonstrating truths in a finite number of steps, and that infinity is often used in the context of limits rather than as a literal value.
  • #1
CozmicScott
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Are zero and infinity the biggest problems for math? Can they ever be the same. zero is infinitly nothing, and infinty stops zero times?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
Zero is a specific number, and infinitely is not a number. Infinitely is what... unboundedness of value?
 
  • #6
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'.
 
  • #7
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
 
  • #8
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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  • #9
schroder said:
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. :grumpy: How long is the real line?

Answers should always be checked, no matter what the answer is.
 
  • #10
Hurkyl said:
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?:devil:
 
  • #11
Hurkyl said:
Bad advice. :grumpy: How long is the real line?

0.208780721 furlong
 
  • #12
Dragonfall said:
0.208780721 furlong

i c wat u did ther, vry clvr
 
  • #13
Hurkyl said:
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.
 

1. What is the concept of infinity in mathematics?

The concept of infinity in mathematics is the idea of a quantity or value that is limitless or endless. In mathematics, infinity is often represented by the symbol ∞ and is used to describe values that are larger than any finite number.

2. What is the "zero vs. infinity problem" in mathematics?

The "zero vs. infinity problem" refers to the difficulty in understanding the relationship between zero and infinity in mathematical calculations. It arises when trying to divide a number by zero or when trying to compare infinitely small and infinitely large values.

3. Can zero be considered as infinity in mathematics?

No, zero cannot be considered as infinity in mathematics. While both zero and infinity represent values that are unbounded and have no fixed magnitude, they are fundamentally different concepts. Zero is a specific quantity that represents nothing, while infinity is a concept that represents something without limits.

4. How does the concept of infinity impact mathematical calculations?

The concept of infinity plays a crucial role in mathematical calculations, particularly in areas such as calculus and number theory. It allows for the representation of infinitely large and infinitely small values, which are essential for solving complex problems and understanding the behavior of functions and equations.

5. Is it possible for a number to be both zero and infinity at the same time?

No, a number cannot be both zero and infinity at the same time. This is because zero and infinity are two distinct concepts in mathematics and cannot coexist simultaneously in a mathematical calculation. However, a limit of a function can approach both zero and infinity as its input approaches a certain value.

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