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Thread: The biggest number is Mathematics

  1. #1 The biggest number is Mathematics 
    Forum Professor leohopkins's Avatar
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    A googol is 10^100 (10 with 100 zeroes after it)

    A googolplex is 10^100^100 (10 with a googol of zeroes after it) - so big infact that there is not enough space in the known universe to write it down.

    However; I have come up with the ULTIMATE BIG number. I call it the "Hopkiplex" (named after me; (who thought it up) - naturally)

    The Hopkiplex is a googolplex to the power of a googolplex; a googolplex of times...i.e. googolplex^googolplex^googolplex^googolplex.....et c....

    The short way of writing down the Hopkiplex will be "hPx" (A lowecase "h", and an upper "P" and a lowercase "x")


    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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    Administrator KALSTER's Avatar
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    I then invent the KALSTERPLEX, which is a Hopkiplex to the power of a Hopkiplex. 8)


    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

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  4. #3  
    Forum Professor leohopkins's Avatar
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    Quote Originally Posted by KALSTER
    I then invent the KALSTERPLEX, which is a Hopkiplex to the power of a Hopkiplex. 8)
    You just HAD to didn't you? :P
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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    and i invent the smallest number which is one divided by a kalster
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  6. #5  
    Forum Freshman pbandjay's Avatar
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    Perhaps the arrow notation would be a simple way of expressing your number.

    http://en.wikipedia.org/wiki/Knuth's_up-arrow_notation



    Where the second Googolplex is the number of powers in the power-tower of the first Googolplex raised to itself. I think the number of powers includes the base as well, so really there are (Googolplex - 1) actual powers in that expression. So I think your number might then be:



    One a side note, how about the....

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  7. #6  
    Forum Radioactive Isotope MagiMaster's Avatar
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    The more interesting thing is that no matter how big of a number we invent, there is always numbers too big to be invented.

    Let's see. Define and , then:
    F(0) = 2
    F(1) = 4
    F(2) = ???
    F(3) = too big

    Seriously, even calculating F(2) is difficult. I think F(3) or F(4) is bigger than the SuperBigPlex though.
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  9. #8  
    Forum Radioactive Isotope MagiMaster's Avatar
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    That's a pretty big number.
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  10. #9  
    Forum Professor leohopkins's Avatar
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    Okay,

    so we now have:

    googol
    googolplex
    hopkiplex
    kalster
    superbigplex

    any more?
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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  11. #10  
    Administrator KALSTER's Avatar
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    Superduperkalsterplex. It is a Kalsterplex to the power of the previously declared highest number, including iterations of itself. 8)
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

    "Gullibility kills" - Carl Sagan
    "All people know the same truth. Our lives consist of how we chose to distort it." - Harry Block
    "It is the mark of an educated mind to be able to entertain a thought without accepting it." - Aristotle
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  12. #11 okay....... 
    Forum Professor leohopkins's Avatar
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    I give up.

    Having said that though, I think I have worked out that it is impossible to multiply or square infinity.....


    Lets assume we live in a multiverse and there are an infinite amount of possibilities that could make up a universe. Does this mean that the chance of a repeating universe is zero? - I think so, as possibilities are infinite, I cant see one being able to repeat...

    Now think of finite possibilities; eventually they would have to repeat, and do so an infinite amount of times....

    So then, I think that this means that infinity^2 is impossible, and thus infinity itself must be one-dimensional or even zero-dimensional. Therefore a singularity could be said to be infinite.

    ** Please note - I am aware that I may get ripped to shreds to mentioning any of the above; but go on go for it ! - Just as long as responses are academic **
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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  13. #12  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Your description doesn't really work because infinity isn't a number. You can't do normal operations on it. There are times and places where it makes sense to do things like , but that's outside the realm of real arithmetic. In general, it's safest to consider infinity as a concept related to, but distinct from, numbers.
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  14. #13  
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    Quote Originally Posted by MagiMaster
    Your description doesn't really work because infinity isn't a number. You can't do normal operations on it. There are times and places where it makes sense to do things like , but that's outside the realm of real arithmetic. In general, it's safest to consider infinity as a concept related to, but distinct from, numbers.
    Not really.

    There is quite a theory of cardinal and ordinal numbers, including an arithemetic. They are ordered, and most of them are infinite. TThere is no single "infinity". There are different sizes of infinity, as with the infinity of the real numbers being larger than the infinity of the integers.

    You run into the same problem there, though. There is no largest cardinal number.

    The real message is that "infiinity" is somewhat subtle, and one needs to understand it or run the risk of reaching unfounded conclusions.

    BTW if people would like a readable treatment of cardiinal and ordinal numbers the book Naive Set Theory by Paul Halmos is highly recommended.
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