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Proof of God thru maths?

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    (Original post by theone)
    Pi is eternal? Do you mean it's decimal never recurs? In which case we know this to be true since we know pi is irrational. The same is true of every irrational number, their decimal representation never repeats. Anyhow, someone mentioned how we don't know what 2 really is, and that it's just a number we associate with a certain property of things. You should really read something by some famous scientific philosopher for information on such things...
    And you should really read some Plato on numbers

    Numbers are still highly debated on in philosophy about what they exactly are, there has been no final conclusion and agreement on what they exactly are. For my own interest could you find out the name of this scientific philosopher, thanks
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    (Original post by Jonatan)
    As I said, infinity and 0 does strange things to numbers. Considder this:

    infinity + 0 = infinity

    Therefore:

    infinity - infinity = 0.

    However:

    infinity + infinity = infinity

    Hence:

    infinity - infinity = infinity.

    And so:

    infinity = 0
    Lol. The problem with all these things is that infinity is not a number, but is being treated as one. Example - how many odd numbers are there? Infinity. How many indices are there? Infinity. Yet the number of indices should be double the number of odd numbers, thus infinity cannot be a numeric definition. I'd also suggest that 0 is not a number either, but much like infinity merely a concept.

    There is however a nice proof for the number line being a circle rather than linear, thus if you keep counting forever you eventually end up back at zero. It's not the same as infinity = 0, more that infinity = -infinity, however already in this infinity is almost being treated as a number (not quite because you can have negative concepts). Getting a circular number line without treating it as a number is hard, although I think I did it once. Might come back tomorrow with proof in hand.
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    (Original post by Harry Potter)
    I've got a joke you might like:


    Hilarious...


    Hahaha, I think that's really funny. Is that worrying?
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    (Original post by pal_sch)
    Nice one! Kinda makes you worry about all the things that rely on such logic to work, like physics and finances.

    No it doesn't. Not if you know there is an entire branch of mathematics concerning infinity, and the mathematicians are perfectly capable of avoiding infinty=0.
    Infinity is not a number like 1,4,8, or pi, or even the square root of -1.
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    (Original post by hitchhiker_13)
    No it doesn't. Not of you know there is an entire branch of mathematics concerning infinity, and the mathematicians are perfectly capable of avoiding infinty=1.
    Infinity is not a number like 1,4,8, or pi, or even the square root of -1.
    But don't you love anoying maths teachers? Especialy when they don't have the maths to disprove it!
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    Just as a lighter side of this, two weeks ago my maths teacher was explaining some sort of weird calculation, and in it stated that 5 x 4 = 40 (I think she got a little confused)
    It makes me laugh whenever I think about it.... hehehe...
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    (Original post by pal_sch)
    But don't you love anoying maths teachers? Especialy when they don't have the maths to disprove it!
    I prefer doing ti with physics teatchers. My favourite example (which annoys me to teh limit as well) is to ask whether objects are gravitationally atracted to light. My argument is that because light has an energy it has an equivalent in relativistic mass. Since mass and energy are two sides of the same thing, all energy should cause a curvature of spacetime and thus all particles carrying energy (also the mass-less bosons) should cause gravitation. However, we know from experience that light does not cause gravitation. If it did, two laser beams would not be able to pass through each other as the distance would approach zero and thus the gravitational force between the laser beams would aproach infinity.
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    (Original post by hitchhiker_13)
    No it doesn't. Not if you know there is an entire branch of mathematics concerning infinity, and the mathematicians are perfectly capable of avoiding infinty=0.
    Infinity is not a number like 1,4,8, or pi, or even the square root of -1.
    Actually you do have algebra with infinities. Also, you have many . DIFFERENT infinities. It was cantor who discovered that you have different infinities and he prooved it with his famous diagonal theorem.

    Considder these two sets. The set off all finite integers, and all finite real numbers. Both sets are finite (There is an infinite amount of finite whole numbers.)

    Now, suppose we start writing a list off all integers and pair them with real numbers between 0 and 1
    Something like this:

    1 - 0.32436154398540...
    2 - 0.47543653543550...
    3 - 0.24534275435438...
    5 - 0.23435436585743...
    and so on....

    Now, lets define a new real number which is constructed in a very special way. The first decimal of this real number will equal the first decimal of tehnbumber that is paired with 1, in the above case this decimal is 3. The second decimal will equal the SECOND decimal of teh number that is paired with 2, in the above case it is 7. You continue like this towards infinity. Now, lets take this new real number and change all teh digits. It doesnt matter how you change them, what is important is that every decimal is different from what it was before. Now, thsi new real number. Lets call it f has an interesting propperty. Its first decimal is NOT equal to the first decimal of the number that is paired with 1. The second decimal is not equal toteh second decimal of teh number that is paired with 2. The thrid decimal is not equal to the third decimal of the number paired with 3 and so on. Thus no integer is paired with f! The new real number is not in the list allthough all the integers are there. The set of real numbers between 1 and 0 cannot be put in one to one correspondence with the integers, yet both are infinite sets. There seems to be different LEVELS of infinities.

    Another wya to view this is to take on the task of listing all the whole numbers, starting at 0. Although it would take an infinite amount of time it is quite easy to do. You may start like this:

    0
    1
    2
    3
    4
    and so on

    This is not possible with real numbers. cus once you have written 0, there is no way to write the "next" number. you may suggest 0.1 , but 0.01 should be before that, and 0.001 should be before THAT. This is quite an effective way to illustrate that although both lists are infinite, they are different kinds of infinities.
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    (Original post by Jonatan)
    Actually you do have algebra with infinities. Also, you have many . DIFFERENT infinities. It was cantor who discovered that you have different infinities and he prooved it with his famous diagonal theorem.

    Considder these two sets. The set off all finite integers, and all finite real numbers. Both sets are finite (There is an infinite amount of finite whole numbers.)

    Now, suppose we start writing a list off all integers and pair them with real numbers between 0 and 1
    Something like this:

    1 - 0.32436154398540...
    2 - 0.47543653543550...
    3 - 0.24534275435438...
    5 - 0.23435436585743...
    and so on....

    Now, lets define a new real number which is constructed in a very special way. The first decimal of this real number will equal the first decimal of tehnbumber that is paired with 1, in the above case this decimal is 3. The second decimal will equal the SECOND decimal of teh number that is paired with 2, in the above case it is 7. You continue like this towards infinity. Now, lets take this new real number and change all teh digits. It doesnt matter how you change them, what is important is that every decimal is different from what it was before. Now, thsi new real number. Lets call it f has an interesting propperty. Its first decimal is NOT equal to the first decimal of the number that is paired with 1. The second decimal is not equal toteh second decimal of teh number that is paired with 2. The thrid decimal is not equal to the third decimal of the number paired with 3 and so on. Thus no integer is paired with f! The new real number is not in the list allthough all the integers are there. The set of real numbers between 1 and 0 cannot be put in one to one correspondence with the integers, yet both are infinite sets. There seems to be different LEVELS of infinities.

    Another wya to view this is to take on the task of listing all the whole numbers, starting at 0. Although it would take an infinite amount of time it is quite easy to do. You may start like this:

    0
    1
    2
    3
    4
    and so on

    This is not possible with real numbers. cus once you have written 0, there is no way to write the "next" number. you may suggest 0.1 , but 0.01 should be before that, and 0.001 should be before THAT. This is quite an effective way to illustrate that although both lists are infinite, they are different kinds of infinities.
    are you sure your net confusing infinitys with infintesimals?

    there is a seperate algebra structure for infintesimals, but none for infinity (as far as im aware)
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    (Original post by Leeroy)
    are you sure your net confusing infinitys with infintesimals?

    there is a seperate algebra structure for infintesimals, but none for infinity (as far as im aware)
    Yes, I am certain. Im nto talking about infinitely small real numbers, Im talking about thefact that there are "more" real numebrs than integers. If you like you could start counting at , say 3. Then you get 3 as teh first real number, but then you cant move on cus no matter what real number , greater than 3 , you pick you will have another real number which is teh average between the previous two. Now, 3 is obviously not an infinitesimal and neither is 3.00000000000000000... infinitely many "0" s .... 00000001. You cannot list tehh real number sin a sequence. Also, considder the diagonal proof as I described above. Cantor labeled the different levels of infinities with the hebrew letter Aleph (uk-learning cant show it). The natural integers is Aleph-0 . Cantor also beleived that the real numbers belonged to the infinity Aleph-1 Now, it has turned out to be impossible to determine whether this is true or not, so set theory is divided in two. Cantorian set theory (Assuming the real numbers are the next in the sequence) and non-cantorian set theory which assumes that there is an infinity (I dont know which kind of infinity) of different Alephs between the whole numbers and teh real numbers.
Updated: April 10, 2004
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