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Concept of Quantity

This is a discussion on Concept of Quantity within the General Discussions forums, part of the Community Boards category; Originally Posted by C_ntua So to clarify one more time, 0.999... cannot be proven to be equal to 1 a) ...

  1. #256
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    Quote Originally Posted by C_ntua View Post
    So to clarify one more time, 0.999... cannot be proven to be equal to 1
    a) Without axioms about infinite sums
    b) Without axioms about decimals with infinite digits
    c) Without something else

    AND if this is attempted the definition of infinity will save 90% of arguing, so people can give their definition of infinity at least in the sense of "infinite decimal digits"
    b implies a, so you could shorten your list, if you want.

    In general, aren't all decimal expansions infinite sums? Decimal representation - Wikipedia, the free encyclopedia

    What makes equations that involve infinity wrong?

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    Registered User KAUFMANN's Avatar
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    Any number multiplied by its inverse is 1 since N*(1/N)=1 because the N's cancel on each other. Now, since 0 is the inverse of infinity, is it safe so assume that 0*infinity=1? Methinks so.

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    Registered User whiteflags's Avatar
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    0 isn't the reciprocal of infinity.

    inf/inf = 1
    1/inf = 0
    0inf = 0

    All of these are made rigorous by the limit concept.

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    Captain Crash brewbuck's Avatar
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    Quote Originally Posted by whiteflags View Post
    0 isn't the reciprocal of infinity.

    inf/inf = 1
    1/inf = 0
    0inf = 0

    All of these are made rigorous by the limit concept.
    They are rigorous if you actually write them as limits. Written in the above way they are just nonsense.
    Code:
    //try
    //{
    	if (a) do { f( b); } while(1);
    	else   do { f(!b); } while(1);
    //}

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    Programming Wraith GReaper's Avatar
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    Think of it this way:
    Think infinity as the universe ( and ignore my signature ).
    The universe is constantly expanding. Likewise, two infinities may not be the same...

    I know... I think... I guess... who am I kidding?
    Devoted my life to programming...

  6. #261
    (?<!re)tired Mario F.'s Avatar
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    Quote Originally Posted by KAUFMANN View Post
    Any number multiplied by its inverse is 1 since N*(1/N)=1
    Except 0. Otherwise...

    0 * (1/0) = 1

    because the N's cancel on each other. Now, since 0 is the inverse of infinity, is it safe so assume that 0*infinity=1? Methinks so.
    Since the above shows you, I hope, that 0 can't be the inverse of infinity (infinity has no inverse), 0 * infinity must be constructed differently. The current agreement is that infinity multiplied by any number, including 0 is undefined.
    The programmer’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.”
    The programmer comes home with 12 loaves of bread.


    Originally Posted by brewbuck:
    Reimplementing a large system in another language to get a 25% performance boost is nonsense. It would be cheaper to just get a computer which is 25% faster.

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    Quote Originally Posted by KAUFMANN View Post
    Any number multiplied by its inverse is 1 since N*(1/N)=1 because the N's cancel on each other. Now, since 0 is the inverse of infinity, is it safe so assume that 0*infinity=1? Methinks so.
    It depends. Do you mean 0 multiplied by something that approaches infinity or something that approaches 0 multiplied by something that approaches infinity? If the former, no, it would be 0. If the latter, sometimes; It could approach anything, because it is an indeterminate form(Indeterminate form - Wikipedia, the free encyclopedia).

    Quote Originally Posted by whiteflags View Post
    inf/inf = 1
    1/inf = 0
    0inf = 0
    lim(x->inf)x/lim(x->inf)x^2 = lim(x->inf)x/x^2 = lim(x->inf)1/x = 0
    The second is correct. (I even used it above.)
    lim(x->inf)1/x * lim(x->inf)x = lim(x->inf)x/x = lim(x->inf)1 = 1

    The first and third are indeterminate, and can't be given a general rule.
    Last edited by User Name:; 04-01-2011 at 12:11 PM.

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