What exactly is infinite

  1. Infinite is more of a concept than a number, but it sometimes apears in mathematical equations and also real life. It almost always destroys anything its in.

    First, I would like to ask some questions about infinite...
    1.) is inf - inf equal to 0?
    2.) is inf times inf = inf squared or just inf?
    3.) is 1/infinite 0?
    4.) is inf. - any real number still inf?
    5,) is inf times any real number still inf?

    Also I have noticed whenever infinite comes into advanced equations or problems that the answer always leads to a paradox or null.

    Real life example 1
    Is their an infinite amount of time?
    If their is, does this mean theirs an infinite amount of space?
    If their is an infinite amount of time, every weird thing you can imagine will happen since infinite times 1/infinite times infinite = 1

    Then again this depends on the six equations I listed above. Please help. Thanks all
     
    Last edited: Jan 11, 2014
  2. jcsd
  3. phinds

    phinds 9,034
    Gold Member

    In real life? Really? Where? Can you think of even one example?
     
  4. I did....
    There's the zenos paradox
    There's an infinite amount of time (possibly$
    There could be an infinite amount of space

    There are more, but I was asking the answer to the six equations not the answer to the examples
     
  5. pwsnafu

    pwsnafu 931
    Science Advisor

    Edit: Before anything else, use "infinity" for the noun. "Infinite" can be used as a noun, but not in the way you want to.

    That is a thought experiment and irrelevant to real life: you can disprove it by walking and touching a wall. It's also irrelevant mathematically: i.e. infinite series completely resolves it.

    Unlikely due to the big bang.

    "Could be" is not good enough, you need observations.


    Infinity in mathematics has multiple definitions, each with different properties and are non-equivalent. For example in the extended real numbers infinity is a number.

    Infinity does not exist as a real number. It does exist in extended reals.

    This is like saying 1/2 does not exist in the integers, hence it destroys the integer mathematics. It does exist in the rationals, hence if you want to work with 1/2 you work in the rationals.

    In the extended reals it is undefined.

    In the extended reals it is equal to infinity.
    In the ordinal numbers it is square of the infinity (note that in the ordinals there are multiple numbers which correspond to infinity).

    On the extended reals, yes.

    On the extended reals, yes.

    In the extended reals, yes.

    None of this is relevant in a mathematics thread because mathematics doesn't deal with the real world.

    Edit: Also there not their. Please learn the difference between there, their and they're.
     
    Last edited: Jan 12, 2014
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  6. Chronos

    Chronos 10,053
    Science Advisor
    Gold Member

    Infinity is a mathematical artifact. It has always proven to be an illusion under careful scientific scrutiny [e.g., quantum physics]. Even the universe, while really big, is observationally finite. Mathematics is a logical extension of reality. Division by zero, the classic definition of infinity, is, however, proven to yield illogical results. When you run into infinities in science, you should question the model.
     
  7. pwsnafu

    pwsnafu 931
    Science Advisor

    If you are saying division by zero leads to contradictions on the real numbers, this is correct.
    If you are saying division by zero leads to contradiction in any mathematical space, that is wrong. See wheel theory.
     
  8. lavinia

    lavinia 2,074
    Science Advisor

    So are you saying that Zeno had no idea that you can walk up to a wall and touch it?
     
    Last edited: Jan 12, 2014
  9. lavinia

    lavinia 2,074
    Science Advisor

    The Shroedinger equation uses continuous time and therefore the concept of infinity. It also uses continuous space.

    This is a philosophical statement and does not belong in the Mathematics Forums - in fact not in any Physics forum.
     
    Last edited: Jan 12, 2014
  10. lavinia

    lavinia 2,074
    Science Advisor

    This is a philosophical statement and does not belong in the Mathematics forum. I'm glad that you know what the real world is though.
     
  11. lavinia

    lavinia 2,074
    Science Advisor

    In Mathematics infinite magnitudes extend the idea of the finite. There are different infinite magnitudes and just like counting numbers, they are ordered by size. The smallest infinite magnitude is the size of the integers. The size of the real numbers is a larger magnitude.

    The idea of infinity is not an "artifact" whatever that means. It has the same rigor as the idea of one or zero or five thousand. To say that the Universe is finite is no more mathematically rigorous than to say that is has the cardinality of the Continuum and in fact that is what is said in Classical Physics including the General and Special Theories of Relativity and in Quantum mechanics and in Quantum Field Theory and in String Theory .....
     
    Last edited: Jan 12, 2014
  12. phinds

    phinds 9,034
    Gold Member

    No, as others have already pointed out, you did not.
     
  13. 1.) is inf - inf equal to 0? No one could tell. If you assume infinities to be equal then they would have to be finite, but they're not so tough luck. Who is to say that one infinity is equal to/lesser than/bigger than the other? There is just no way you can tell.
    2.) is inf times inf = inf squared or just inf? How could you add to something or multiply infinity by something if you don't know how much that "infinity" contains. Operations work with finite figures.
    3.) is 1/infinite 0? Yes and no. In limit calculations you can say it is 0 because limits estimate the boundary, but just having 1/infinity is undefined.
    4.) is inf. - any real number still inf? Undefined. Imagine if you have an expression of 3y - 2z. Try subtracting 10 elephants from 52 motorcycles - you do have the expression, but it means nothing.
    5,) is inf times any real number still inf? again, undefined.
    Don't think of infinity as some sort of number. It is just a concept - it doesn't obey any rules in maths.

    Another example of the concept of infinity - how much energy do you need to reach the speed of light? An infinite amount. Wait what? How much is infinite? Exactly.
     
    Last edited: Jan 12, 2014
  14. If you say infinite doesn't appear in mathematics and real life we have to agree to disagree. It seems "there" (not their, turning off autocorrect helps my grammar a lot) is no straightforward answer to the equations I have asked. I didn't quite feel anyone have a direct explanation.

    Whats the definition of infinite? Endless number, limitless(not a mathmatical limit), or is infinite a number eg 10^10^10^10^10?

    One reply said their is not an infinite amount of time because of the Big Bang. Well this depends on what time is and your personal opinion is. Assuming the Big Bang is real; If you can say "before the Big Bang" you can say time has no beggining or end.

    The same reply I believe said/suggested their is not an infinite amount of space. This is beyond me. Thats like saying our earth is flat and you can not go beyond the edge.
     
    Last edited: Jan 12, 2014
  15. mfb

    Staff: Mentor

    The surface of earth is a good example of a finite area without a boundary. The universe could have the same shape (just with one more dimension of course), we don't know.

    Nothing of that.
    Infinity (note the spelling).
     
  16. 10n is perfectly finite as long as n is finite add however many powers of finite figures as you want. You can't make an infinite figure out of finite material.
     
  17. I suggest the OP disregard this post, I struggle to find one correct statement.
     
  18. It is never wrong to prove others wrong. Just by saying "you are wrong" is not enough in my case.
     
  19. CompuChip

    CompuChip 4,297
    Science Advisor
    Homework Helper

    I suggest the OP stop treating infinity as a number, like 2, that you can multiply by another number, like 7, and get a sensible answer.
    In "standard" mathematics (i.e. up to somewhere in an Analysis 2 course at University level) infinity is not a number, but a concept. It is the result of a limit process that can be well-defined, and that we can give a name, but we shouldn't treat the limit as an element of the sequence that produces that limit. Infinities can be really slippery to work with, and in mathematics you need to resort to e.g. extended reals, as mentioned earlier, to do it properly. In physics they're usually just a big head ache as they don't represent anything physical as far as we are aware, and any theory that yields unbounded observables is in trouble.
     
  20. lavinia

    lavinia 2,074
    Science Advisor

    Infinity is not a Real number. But neither is i or the unit quaternions. Nevertheess infinite ordinal numbers are well defined numbers.
     
  21. CompuChip

    CompuChip 4,297
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    Homework Helper

    I know lavinia, but they're not part of the real numbers, and the usage of statements like "inf - inf = 0" strongly suggests to me that the OP is not ready to be introduced to the mathematical details without a conceptual understanding of why infinity can not be treated that way without additional tools.
     
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