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Thread: the case of infinity

  1. #1 the case of infinity 
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    What is the value of : (given that x is a number)

    1). ∞ / 0
    2).
    0 /
    3). ∞ / ∞
    4). ∞ + 0
    5). ∞ - 0
    6). 0 - ∞
    7). x / ∞
    8). ∞ / x
    9). ∞^∞ (exponent)
    10). (root) ∞


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  3. #2  
    Moderator Moderator Markus Hanke's Avatar
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    None of these is defined; they make no sense. "Infinity" is not a number that can be used and manipulated like other numbers.


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  4. #3  
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    Quote Originally Posted by YNuwara View Post
    What is the value of : (given that x is a number)

    1). ∞ / 0
    2).
    0 /
    3). ∞ / ∞
    4). ∞ + 0
    5). ∞ - 0
    6). 0 - ∞
    7). x / ∞
    8). ∞ / x
    9). ∞^∞ (exponent)
    10). (root) ∞
    3 is undetermined. Others are 0 or ∞ or -∞ (all obvious). For some ∞, the sign is undetermined.
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  5. #4  
    Forum Professor Daecon's Avatar
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    Think of all the numbers possible. There's an infinity of them.

    Now, think of all the numbers that are divisible by 2 (the "even" numbers), there's also an infinity of them, as well.

    What's one infinity divided by the other? Is it 2? Is it one-half?

    What about all the numbers that are divisible by 3? By 4? By 5? All the numbers divisible by [any number you can think of]?

    Now, how many possible "numbers in infinity, that are divisible by this number" numbers are there? There's an infinite amount of numbers in infinity you can divide infinity by... in order to divide infinity by this other number.

    (Now, try saying that ininfite times fast.)
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  6. #5  
    Forum Junior anticorncob28's Avatar
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    I personally know no rule of mathematics stating that addition and multiplication only apply to the complex numbers. If this is in fact true, then I can create my own algebra which counts infinity as something that can be operated on, and there's nothing wrong with it until an inconsistency is found. For these answers, I will assume a countable infinity is what is meant by these questions.
    1) You are asking the solution to 0x = infinity. A real number line contains a continuum infinity number of points all with length zero, yet all the points together have length infinity, so beth_1 is a solution for x.
    2) A countable infinity of points cannot solidly fill in a line segment. Thus, 0*infinity = 0 if it is the countable infinity, so the answer is zero.
    3) If you multiply infinity by any positive number, you get infinity again, so the answer is any positive number, or indeterminate.
    4) If you have infinity rocks, and add nothing more, you still have infinity rocks.
    5) If you have infinity rock, and take away nothing, you still have infinity rocks.
    6) A + B is defined as A + (-B) and -B is the inverse of B such that B + -B = 0. Infinity + -infinity can equal anything, including zero, so the inverse is -infinity, and this is 0 + (-infinity) = -infinity.
    7) Infinity multiplied by any positive number is infinity, by any negative number is negative infinity, and by zero is zero, and thus no non-zero real number. This operation is undefined.
    8) Any positive real number, as any positive number multiplied by infinity is infinity.
    9) The continuum infinity, same as 2^infinity or 10^infinity. Beth_1
    10) Infinity*infinity = infinity (the set of integers is the same size as the set of ordered pair integers), thus sqrt(infinity) = infinity.
    More can be seen at:
    Math Forum - Ask Dr. Math
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  7. #6  
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    If you really, really want to include infinity as a number it's been done several times before leading to things like the hyperreal numbers and the surreal numbers. But once you go that route, you start losing important pieces of common-sense-logic built into the real numbers. Things like the ability to say whether one number is bigger than another. In the surreals, * (called star) is a distinct number but it is neither bigger nor smaller than 0.

    The simplest of these is the one (or two) point compactification of the real line, but these are not groups like the integers, rationals, reals, complex or surreals. Extended real number line - Wikipedia, the free encyclopedia
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  8. #7  
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    Quick rant on dividing by zero, why you can strike off example 1: zero is orthogonal to the real number line... Which is to say, it exists in its own dimension. zero lives in a zero dimensional space, every other real numbers lives in a one dimensional space (the real number line). If you divide 6 by 2, your asking how many vectors of length 2 must be added to get to the point 6 (3). If you divide 6 by zero, you're asking how many zero vectors must be added. But remember, they're orthogonal, 0-vectors don't go down the number line, they live in a point. So there's no amount of them you can add to get to 6, just as there's no amount of real numbers you can add to get to I, the imaginary unit, which is also orthogonal to the real numbers. In other words, no amount of travelling directly east or west will ever take you north, no amount of travelling in 2D flatland will ever take you into the third dimension, no amount of frequent flyer miles will get you into the 4th dimension. No amount of movement in a point (zero dimension) can ever get you anywhere, and dividing asks how many steps a size you need to take to get somewhere. So divide by zero is not a number.
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  9. #8  
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    Two separate quantities ,each equaling 0, going on to be represented as 0, the separateness dissolving, looks flawed. I am starting to agree with Marcus again.
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  10. #9  
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    There are an infinite different sizes of infinity.
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  11. #10  
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    Folding technique :
    Equal fold always provides chance of EIGHT times . Not more than that

    So, LIMIT is 8

    Is it possible you can apply that logic here on INFINITY too.

    Dividing or folding Infinite equally eight times ...... Can this be imaginable .
    Is it applicable to Infinity too. Reaching half of INFINITY is just imaginable like infinity / 2 .

    using this assumption of folding or division technique , is it possible to find LIMIT !!!!!! on INFINITY TOO !!!!!!!!!!!!!!!!!

    logically i meant !!!!! ya it's still laughable , if you say , ya it is possible !
    and meaningless if you say no . don't ask why ?!!

    LIMIT to INFINTY !!!
    Result may be - Infinity which cannot be folded !!!

    Just logic .
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  12. #11  
    Bullshit Intolerant PhDemon's Avatar
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    Logic? More like gibberish, this makes no sense, try again in English.
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  13. #12  
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    Quote Originally Posted by sciencestudy View Post
    Folding technique :
    Equal fold always provides chance of EIGHT times . Not more than that

    So, LIMIT is 8
    Didn't Mythbusters exceed that limit?
    There are no paradoxes in relativity, just people's misunderstandings of it.
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  14. #13  
    Brassica oleracea Strange's Avatar
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    Britney Gallivan - Wikipedia, the free encyclopedia "is best known for determining the maximum number of times that paper or other materials can be folded in half. ... She served as a consultant and was mentioned in an episode of MythBusters"
    ei incumbit probatio qui dicit, non qui negat
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  15. #14  
    Forum Professor river_rat's Avatar
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    Quote Originally Posted by anticorncob28 View Post
    I personally know no rule of mathematics stating that addition and multiplication only apply to the complex numbers. If this is in fact true, then I can create my own algebra which counts infinity as something that can be operated on, and there's nothing wrong with it until an inconsistency is found. For these answers, I will assume a countable infinity is what is meant by these questions.
    1) You are asking the solution to 0x = infinity. A real number line contains a continuum infinity number of points all with length zero, yet all the points together have length infinity, so beth_1 is a solution for x.
    2) A countable infinity of points cannot solidly fill in a line segment. Thus, 0*infinity = 0 if it is the countable infinity, so the answer is zero.
    3) If you multiply infinity by any positive number, you get infinity again, so the answer is any positive number, or indeterminate.
    4) If you have infinity rocks, and add nothing more, you still have infinity rocks.
    5) If you have infinity rock, and take away nothing, you still have infinity rocks.
    6) A + B is defined as A + (-B) and -B is the inverse of B such that B + -B = 0. Infinity + -infinity can equal anything, including zero, so the inverse is -infinity, and this is 0 + (-infinity) = -infinity.
    7) Infinity multiplied by any positive number is infinity, by any negative number is negative infinity, and by zero is zero, and thus no non-zero real number. This operation is undefined.
    8) Any positive real number, as any positive number multiplied by infinity is infinity.
    9) The continuum infinity, same as 2^infinity or 10^infinity. Beth_1
    10) Infinity*infinity = infinity (the set of integers is the same size as the set of ordered pair integers), thus sqrt(infinity) = infinity.
    More can be seen at:
    Math Forum - Ask Dr. Math
    You are mixing extended real arithmetic with cardinal arithmetic and coming up with some weird solutions as a result.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  16. #15  
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    PH DEMON quote
    "Logic? "



    Infinity is a matter of logic in mathematics .

    There exists great formula to prove that EXISTENCE OF UNIVERSE IS FINITE.
    This formula is obtained by depending on subject of mathematics Which involves the LOGIC OF INFINITE AS CORE PART OF IT !!!!!


    Now , how come one can rely on LOGIC OF INFINITENESS EXISTENCE (IMAGINABLE)
    TO PROVE THAT REAL EXISTENCE IS FINITE (PRACTICAL)

    ya , it was just a logic of arguement !!!.....
    ....... used to prove that real existence being called finiteness is baseless !!!

    1. Math got INFINITENESS .
    2. CONSERVATION OF MASS THEORY uses MATH LOGIC .
    3 . So , CONSERVATION OF MASS THEORY somehow and somewhere relates itself with INFINITENESS LOGIC
    to prove itself as being real , i.e., FINITE

    A=B : B=C
    so , A = C ;

    Imaginable = X ;
    X = Real ;
    So, Imaginable = Real !!!!


    That's what logic is all about .
    But Reality may be different.
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  17. #16  
    Bullshit Intolerant PhDemon's Avatar
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    This is also gibberish and has little (anything?) to do with the original gibberish except mentioning infinity as far as I can see. Are you high?
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  18. #17  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by sciencestudy View Post
    That's what logic is all about .
    But Reality may be different.
    Huh ?!
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