Infinity

Discussion in 'Physics & Math' started by wegs, May 30, 2019.

  1. wegs Matter & Pixie Dust Valued Senior Member

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    So, I have a question.

    Is infinity the largest number there is, or is it not a number at all?
     
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  3. sculptor Valued Senior Member

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    if memory serves:
    x divided by infinity = 0
    x divided by 0 = infinity

    is zero a number?
     
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  5. DaveC426913 Valued Senior Member

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    It is not a number at all. At least, it is not one we use in our standard mathematics.
    It is possible to use mathematical systems that use infinities, you just have to be sure to define what system you're using.
     
    Last edited: May 30, 2019
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  7. DaveC426913 Valued Senior Member

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    No. You cannot use infinity in arithmetic operations. And you cannot divide by zero.
    x divided by infinity = undefined
    x divided by 0 = undefined



    There is a proof of this, if I can remember what it is...

    The operation of division is defined as the inverse operation of multiplication:
    https://simple.wikipedia.org/wiki/Division_(mathematics)

    So, if you can't multiply it, you can't divide it.

    Q: What number times infinity gives you x?
    A: There is no unique number that can be used.
    IOW, such a number is not defined.

    Q: What non-zero number times zero gives you x?
    A: There is no unique number that can be used.
    IOW, such a number is not defined.
     
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  8. wegs Matter & Pixie Dust Valued Senior Member

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    Okay, so if you were to add 1 to infinity, it would remain infinity.

    I wonder if the life span of the most futuristic humans will ever see infinity materialize. So, when do we stop “counting?” lol What number precedes infinity?
     
  9. DaveC426913 Valued Senior Member

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    Well, you can't, really. That would be an arithmetic operation.

    Even the age of the universe won't be infinity.



    What I think is more cool than infinity is very very large numbers.

    Graham's Number had the dubious distinction of being the largest number ever invoked in a serious mathematical problem.

    It makes a Googol look like zero. And it makes a Googolplex look like zero too.

    Graham's number is so large that it cannot physically be written in our numbering system even given the volume of the universe to write in.

    It required a whole new form of notation just to represent it. Even using this notation, the Wiki article balks at writing the whole thing out; it simply puts an ellipsis (...) for the middle part.

    Graham's number is the upper bound on the answer of a problem in the mathematical field of something called Ramsey theory (something to do with connecting vertices of lines). The author points out that this is the upper limit on the number, and that the actual number is more likely ... six.
     
    Last edited: May 30, 2019
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  10. wegs Matter & Pixie Dust Valued Senior Member

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    Ha I agree, that is cool. Maybe as cool as the concept of infinity.

    Or maybe as cool as “aleph null,” the smallest infinite number.

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    That’s actually just confusing.

    What is an infinite set?
     
  11. gmilam Valued Senior Member

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    Infinity is a concept. Apparently there can even be different sizes of infinities

    The set of all even numbers is infinitely large.
    The set of all positive even numbers is infinitely large, but only half the size of the previous infinity.
     
  12. Michael 345 New year. PRESENT is 69 years old Valued Senior Member

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    According to a British TV program QI 0 zero is a number

    It is a even number as it sits between two odd numbers

    1 and -1

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  13. DaveC426913 Valued Senior Member

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    Yup. It is both a whole number and an integer.
     
  14. wegs Matter & Pixie Dust Valued Senior Member

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    Is infinity ...stagnant, meaning it isn’t continuously increasing? Not sure how to word that.
     
  15. arfa brane call me arf Valued Senior Member

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    Infinity makes addition and multiplication meaningless. But, if you make infinity something you can never reach, then arithmetic can be defined anywhere there are, um, sufficiently large sets of finite numbers.

    But the set of all finite numbers must be infinite, a set can be infinite although none of its elements are. Such sets can be proven infinite by induction.
    Induction is something that doesn't "go to" infinity because it doesn't have to, it only has to show there is no largest finite number.
    The question isn't meaningful, infinity doesn't increase or decrease.
    Sorry about that.
     
    Last edited: May 30, 2019
  16. wegs Matter & Pixie Dust Valued Senior Member

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    I think there is a misconception about infinity, that it increases. That it has no end. But there is an end, right? It is just outside of natural numbers.
     
  17. DaveC426913 Valued Senior Member

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    Sure. No matter how large a number you have, you can always add 1 to it.
    This applies to any number, just not to infinity, (since you can't use infinity in arithmetical operations.)
     
  18. DaveC426913 Valued Senior Member

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    Having no end is not the same as increasing.
    A circle has no end, but it does not increase.

    Increasing implies change over time. Not sure what that has to do with infinity.
     
  19. gmilam Valued Senior Member

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    I'm not a mathematician, I am a computer programmer by trade. But in my understanding, infinity is not an amount.

    Positive integers may start at 1, but there is no largest number at the other end.. you can always add 1 more. A graph of whole numbers would stretch out infinitely in both directions from zero. Both sets are infinitely large, even though the second set is "obviously" twice as large as the first.

    The number of fractions between 1 & 2 is infinite. You can always increase the denominator to get a smaller fraction - or add another digit to the right of the decimal point.
     
  20. sculptor Valued Senior Member

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    ok
    an even number with some rather peculiar properties?
     
  21. RainbowSingularity Valued Senior Member

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    i want you to choose a random number between 0 & infinity

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  22. wegs Matter & Pixie Dust Valued Senior Member

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    Okay, so basically - there hasn't ever been a math equation that could yield an infinite result. And there never will be. So, it's just a term to explain something out of bounds.

    Thanks for helping make sense of it, everyone.
     
    Last edited: May 31, 2019
  23. DaveC426913 Valued Senior Member

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    The usual way this is phrased is that such an operation will result in values rising "without limit", or "with no upper bound" or "limit approaches infinity".

    Well, there's lot of things you can do with infinities, its just that combining them with real numbers in arithmetical operations isn't one of them.
     

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