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Math Help - Infinity

  1. #1
    Member Chokfull's Avatar
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    Infinity

    Does anyone know why Infinity is not classified as a real number?
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    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Chokfull View Post
    Does anyone know why Infinity is not classified as a real number?
    But, isn't it clear? Infinity is an idea. It represents a number that can never be reached in reality, and therefore, is not real.
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  3. #3
    Member Chokfull's Avatar
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    Saying you can't reach infinity is the same as saying you can't rotate a line 90 degrees! do this to a line, making it vertical, and you have a slope of infinity, \tan 90, or \frac {1} {0}. infinity is a value that can be used in math.
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    No one in Particular VonNemo19's Avatar
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    Sir, by definition, a line is infinite, no matter what it's position. I recomend you have a look at this:

    infinite definition | Dictionary.com

    Maybe this will help you.


    By the by, infinity, by DEFINITION, is immeasureable. Nubers are measurements of magnitude. Therefore, inifity is not a number. Now that's Logic 101.

    Oh, what do we say about \tan\frac{\pi}{2}?

    It's undefined.
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  5. #5
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    Quote Originally Posted by Chokfull View Post
    Saying you can't reach infinity is the same as saying you can't rotate a line 90 degrees! do this to a line, making it vertical, and you have a slope of infinity, \tan 90, or \frac {1} {0}. infinity is a value that can be used in math.
    You may enjoy reading about hyper real numbers as used in non-standard analysis.
    Here is a website from which you can download for free a calculus textbook based on their use.
    Chapter one contains the material you may be interested in.
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    Quote Originally Posted by Chokfull View Post
    Does anyone know why Infinity is not classified as a real number?
    The basic reason why ∞ cannot be included in the real number system is that it would violate the rules of arithmetic. For example, ∞ + 1 = ∞. Subtract ∞ from both sides and you get 1 = ∞ ∞. But it's equally true that 2 + ∞ = ∞, and then if you subtract ∞ from both sides you find that 2 = ∞ ∞. Put those two conclusions together and you get 1 = 2, which doesn't look good.

    So either the whole of arithmetic has to be redesigned, or ∞ has to go. Mathematically, it's no contest. Infinity has to go.
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  7. #7
    Member Chokfull's Avatar
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    Quote Originally Posted by VonNemo19 View Post
    Sir, by definition, a line is infinite, no matter what it's position. I recomend you have a look at this:

    infinite definition | Dictionary.com

    Maybe this will help you.


    By the by, infinity, by DEFINITION, is immeasureable. Nubers are measurements of magnitude. Therefore, inifity is not a number. Now that's Logic 101.

    Oh, what do we say about \tan\frac{\pi}{2}?

    It's undefined.
    I'm assuming you meant "numbers"

    Numbers are not always "measures of magnitude." You can't measure negative numbers, yet they still count. And saying something is undefined is a cheap way of ignoring something you dont understand.

    Quote Originally Posted by Opalg View Post
    The basic reason why ∞ cannot be included in the real number system is that it would violate the rules of arithmetic. For example, ∞ + 1 = ∞. Subtract ∞ from both sides and you get 1 = ∞ ∞. But it's equally true that 2 + ∞ = ∞, and then if you subtract ∞ from both sides you find that 2 = ∞ ∞. Put those two conclusions together and you get 1 = 2, which doesn't look good.

    So either the whole of arithmetic has to be redesigned, or ∞ has to go. Mathematically, it's no contest. Infinity has to go.
    Negative numbers and zero also often defy the rules of math, yet they are still numbers
    Last edited by mr fantastic; May 29th 2009 at 03:58 AM. Reason: Mereged posts
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  8. #8
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Chokfull View Post
    Negative numbers and zero also often defy the rules of math, yet they are still numbers
    Listen man, I'm not going to hang around any longer. Wikipedia could answer your questions better than any of us can; so go there. Look up infinity or real numbers or something, and have a coke and a smile.
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  9. #9
    Member Chokfull's Avatar
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    Nice way to quit, but I'm not allowed Coke--too caffeinated, my parents say I'll get hyper

    Also, Wikipedia gives information, but won't let me present what I think.

    By, the way, Plato, I'll check out that site when I get a chance. Thanks!
    Last edited by mr fantastic; May 29th 2009 at 03:56 AM. Reason: Merged posts
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  10. #10
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    Quote Originally Posted by Chokfull View Post
    Negative numbers and zero also often defy the rules of math, yet they are still numbers
    What rules of math are you referring to? If you mean things like "you can't take the square root of a negative number" or "you can't divide by 0", there are no "rules of math" that say you can.

    The set of real numbers forms a "complete ordered field". The "rules of math" for the real numbers are precisely those of a complete, ordered, field:
    1) The real numbers form a commutative group under addition.
    _____a) (x+ y)+ z= x+ (y+ z)
    _____b) x+ y= y+ x
    _____c) there exist a number, 0, such that x+ 0= x for all x
    _____d) for every x there exist a unique y such that x+ y= 0

    2) xy= yx
    3) there exist a number, 1, such that 1x= x for all x
    4) For every x except 0, there exist y such that xy= 1
    5) x(y+ z)= xy+ xz

    6) There exist an order x< y such that
    ____a) if x< y then x+ z< y+ z
    ____b) if x< y and 0< z then xz< yz
    ____c) for any two number x and y, one and only one of
    _______i) y= x
    ______ii) x< y
    _____iii) y< x
    is true.

    7. All Cauchy sequences converge.

    Which of those do negative numbers or 0 "defy"?
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  11. #11
    Member Chokfull's Avatar
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    Yes, you're right. Sorry, I mistyped. I meant "rules of arithmetic." I meant they just don't follow normal rules in many cases. Also, Infinity follows all those rules you just stated, so it is a real number.

    I thought you were leaving, von_nemo, but you're still coming back, as the thanks to hallsofivy show.
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  12. #12
    Member Chokfull's Avatar
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    I went to wikipedia and found "Real numbers can be thought of as points on an infinitely long number line." An infinite number line would include infinity.

    The number line is infinite. thus, infinity must be part of the number line. it is the only number which can reach far enough to fill the "last" spot.

    .................................................. .................................................. ....... Oooookay... I'm gonna assume i'm right, but check about once a week.
    Last edited by Chokfull; June 3rd 2009 at 02:59 PM.
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  13. #13
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    Quote Originally Posted by Chokfull View Post
    I went to wikipedia and found "Real numbers can be thought of as points on an infinitely long number line." An infinite number line would include infinity.

    The number line is infinite. thus, infinity must be part of the number line. it is the only number which can reach far enough to fill the "last" spot.

    .................................................. .................................................. ....... Oooookay... I'm gonna assume i'm right, but check about once a week.
    You are not right.

    A number line extends in both directions INDEFINITELY. We call this indefinite length "infinitely long".

    Numbers, by definition, are DEFINITE lengths on the number line.

    Since infinity is not defined by a definite amount, it can not be a number.
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  14. #14
    Grand Panjandrum
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    Quote Originally Posted by Chokfull View Post
    Yes, you're right. Sorry, I mistyped. I meant "rules of arithmetic." I meant they just don't follow normal rules in many cases. Also, Infinity follows all those rules you just stated, so it is a real number.
    No it does not. Try checking them.

    CB
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  15. #15
    Member Chokfull's Avatar
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    Which rule does it not obey? I looked them over again...

    And look at my previous post about undefined... it is about the same with indefinite
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