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1 = 2.

  • 07-04-2003 7:31pm
    #1
    Banned (with Prison Access) Posts: 18,300 ✭✭✭✭Seaneh


    I will now demonstrate that 1 is equal to 2.

    Ahem.
    If a = 1, and b = 1, then...

    a = b = 1

    Multiplying both sides by "a" gives...

    a2 =ab

    Now, let's subtract b2 from both sides...

    a2 - b2 = ab - b2

    Factoring out both sides leads us to...

    (a+b)(a-b) = b(a-b)


    Next, we divide both sides by (a-b) and get...

    a + b = b

    Substituting 1 for A and B brings us...

    1 + 1 = 1

    Therefore...

    2=1.

    There you have it folks!
    Wasn't that just the fun-est thing you've done in weeks?
    I already know that it's a flawed equation. But do any of you know why?


«1

Comments

  • Banned (with Prison Access) Posts: 18,300 ✭✭✭✭Seaneh


    considering you can't divide a-b, since a-b=0 and a zero in the denominator gives no real solution, it's rather impossible for 1=2, or for you to get a real solution from that equation


  • Registered Users Posts: 1,562 ✭✭✭Snaga




  • Business & Finance Moderators, Entertainment Moderators Posts: 32,387 Mod ✭✭✭✭DeVore


    Originally posted by Gandalf/Sean
    Next, we divide both sides by (a-b) and get...


    Thats your error... a-b = 0

    Anything divided by 0 gives an error.

    Alternatively (if you tried to use a cancelation argument to avoid being hoist by the division-by-zero petard) I can argue:

    (a+b)(a-b) = b(a-b)

    Since (a-b)=0 this can be rewritten (a+b)(0) = b(0)
    which reduces to the trivial 0=0.



    you can annoy mathematicians in a better way by suggesting:

    since infinity is the largest number known to man infinity + 1 must equal infinity and then subtract "infinity" from both sides leaving 1=0.

    Be prepared to get studiously ignored or hit on the head (I prefer the hitting approach).

    DeV.


  • Business & Finance Moderators, Entertainment Moderators Posts: 32,387 Mod ✭✭✭✭DeVore


    Bah snaga... some of us use the aul grey matter! :)
    *mutter* computers... never catch on ... what is this interweb malarkey anyway *mutter*


    DeV.


  • Business & Finance Moderators, Entertainment Moderators Posts: 32,387 Mod ✭✭✭✭DeVore


    Must learn to write shorter replies.

    DeV.


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  • Closed Accounts Posts: 2,155 ✭✭✭ Raylan Modern Pane


    hehe infinty is not number/variable?


  • Registered Users Posts: 857 ✭✭✭kamobe


    a = b = 1

    Multiplying both sides by "a" gives...

    a2 =ab

    Multiplying both sides by a gives you (a)(a)=(a)(b)
    which equates to (1)(1)=(1)(1)

    and 1=1

    a*a is not equal to 2a :)


  • Business & Finance Moderators, Entertainment Moderators Posts: 32,387 Mod ✭✭✭✭DeVore


    I think he was using a2 to mean a^2 ("a" squared)...

    DeV.


  • Banned (with Prison Access) Posts: 23,556 ✭✭✭✭Sir Digby Chicken Caesar


    i doodled something like this in math class years ago, it freaked me out when I saw it at first. i had to go to the teacher to ask wtf I had done hehe


  • Registered Users Posts: 857 ✭✭✭kamobe


    I think he was using a2 to mean a^2 ("a" squared)...

    DeV.

    I was thinking that having looked at the link :D


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  • Closed Accounts Posts: 7,563 ✭✭✭leeroybrown


    But b cannot be 1:

    a + b = b

    Therefore a = 0


    Equally you have proved that 0 = 0.

    Making b = 0

    But that ain't exactly proper maths either ;)


  • Registered Users Posts: 1,562 ✭✭✭Snaga


    Originally posted by DeVore
    Bah snaga... some of us use the aul grey matter! :)
    *mutter* computers... never catch on ... what is this interweb malarkey anyway *mutter*


    DeV.

    Ah yes, I should have titled it 'The internet makes _me_ stupid', or at least very very lazy :) (/me huggles google)


  • Registered Users Posts: 601 ✭✭✭honeymonster


    Me maths teacher gave me this one

    4 - 10 = 9 - 15
    4 - 10 + 25/4 = 9 - 15 + 25/4
    (2 - 5/2)² = (3 - 5/2)²
    2 - 5/2 = 3 - 5/2
    2=3


  • Registered Users Posts: 233 ✭✭Congoose


    (2 - 5/2)² = (3 - 5/2)²
    2 - 5/2 = 3 - 5/2
    That is class! :)
    I think this one is about positive and negative square roots.

    R.H.S.
    (3-5/2) is a positive number (1/2). Square it and you get 1/4. Here, the square root is taken to be (3 - 5/2 = +1/2), so you are taking the positive square root of 1/4.

    L.H.S.
    (2-5/2) is really a negative number (-1/2). When you square this you get 1/4. Here the square root is deemed to be (2 - 5/2 = -1/2), which is the negative square root of 1/4.

    When taking the square root of both sides of an equation, you must take both positive square roots or both negative square roots. This would give you: 1/2 = 1/2 or -1/2 = -1/2. So it is true!

    This example takes negative root on the L.H.S. and positive root on the R.H.S., so it's not allowed. Does this make sense or am I going around in circles? :confused:


  • Registered Users Posts: 68,317 ✭✭✭✭seamus


    Originally posted by SearrarD
    hehe infinty is not number/variable?

    Infinity isn't a number in the normal sense of the word. Normal operations have no effect on it.

    Infinity +10 = Infinity
    Infinity -10 = Infinity
    Infinity/10 = Infinity
    Infinity * 10 = Infinity

    It's generally accepted that

    10/Infinity = 0
    Infinity/Infinity = Infinity (I think)
    Infinity * Infinity = Infinity
    Infinity + Infinity = Infinity
    Infinity - Infinity = Infinity (I think)


  • Registered Users Posts: 35,523 ✭✭✭✭Gordon


    but multiply infinity by 8 and you get a nice 4 leaf clover.

    *ahem*


  • Closed Accounts Posts: 14,483 ✭✭✭✭daveirl


    This post has been deleted.


  • Registered Users Posts: 427 ✭✭Epitaph


    Infinity/Infinity = Infinity (I think)

    I don't think so. I'd imagine you should get 1, it all depends on the "scale" of infinity being discussed.

    Fecking maths => TEH DODGY!!


  • Registered Users Posts: 1,328 ✭✭✭Sev


    Hehe, me and Davey (PHB) have this running joke now about the value of 0/0

    Some say its 0 as its 0 over a number. Some say its infinity because its a number over 0, and some say its 1. Its essentially infinity/infinity, which is the same as 6/6 which is the same as 5/5 which equals 1, so as far as im concerned the answer is 1.

    But the question is so utterly stupid and trivial, I like to think of it as a question of faith. What do you believe?


  • Registered Users Posts: 35,523 ✭✭✭✭Gordon




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  • Closed Accounts Posts: 14,483 ✭✭✭✭daveirl


    This post has been deleted.


  • Registered Users Posts: 15,443 ✭✭✭✭bonkey


    Originally posted by Congoose
    This example takes negative root on the L.H.S. and positive root on the R.H.S., so it's not allowed. Does this make sense or am I going around in circles? :confused:

    Dont be confused.

    If a² = b², then a = +/- b.
    or, if you prefer :
    If a² = b², then abs(a) = abs(b).

    Not

    If a² = b², then a = b.


    Its more or less what you mentioned, though....just slightly more formal.

    jc


  • Registered Users Posts: 1,328 ✭✭✭Sev


    Originally posted by daveirl
    Infinity isn't a numeric value it's a concept.
    Anything divided by 0 is undefined BTW

    Infinity/Infinity, technically, is not 'undefined' but 'indeterminate'. Mathematics breaks down with these numbers, so dont get caught up on definitions and technicalities and what some smartey maths dude says is correct. It's all nonsense and 'undefined' anyway, and the values you might assign to these expressions will ultimately depend on their practical application. But nevermind, you seem to have just missed the jest of my post.


  • Closed Accounts Posts: 14,483 ✭✭✭✭daveirl


    This post has been deleted.


  • Registered Users Posts: 1,328 ✭✭✭Sev


    Sure they are, 0 is a number, a number smaller the any other number. Infinity could be considered its reciprocal: a number greater than any other number.

    But yes, Infinity can never really physically exist. Anyway I think it's pretty trivial debating this any further.


  • Moderators, Social & Fun Moderators Posts: 10,501 Mod ✭✭✭✭ecksor


    Talking about physical existence is irrelevant.

    If infinity is a number, as you claim, then which set does it belong to? And how are the arithmetic operations (or just division) defined on that set?


    From your comments that this all depends on practical explanations and not to believe what smartey maths people tell you, I have a feeling that you're talking about some sort of notion of infinity that exists in your head rather than anything you can express mathematically, which is fine, but you should make it clear that this is the case.


  • Registered Users Posts: 12,309 ✭✭✭✭Bard


    Originally posted by Sev
    Sure they are, 0 is a number, a number smaller the any other number.

    Really? Oh...

    thanks for clearing that up, 'cos... y'see... I thought negative numbers were 'smaller' than zero.

    Infinity could be considered its reciprocal: a number greater than any other number.

    Wouldn't 'minus infinity' be infinity's reciprocal?

    As for zero, the opposite of 'nothing' isn't necessarily 'everything'. It could merely be 'something'.

    But yes, Infinity can never really physically exist. Anyway I think it's pretty trivial debating this any further.

    As ecksor said physical existence has nothing to do with it. Infinity exists in mathematics - that is what counts.


  • Registered Users Posts: 1,328 ✭✭✭Sev


    Oh sweet jesus. Exactly, thats all Im saying.

    Surely there will be procedure and rules governing how operations involving infinity will be carried out in different circumstances. And there will be strict mathematical standards and definitions. But these are subjective and really bare no relevance if you have a concrete grasp of the idea of infinity and know how it might apply to your particular calculation.


  • Registered Users Posts: 1,328 ✭✭✭Sev


    Originally posted by Bard
    thanks for clearing that up, 'cos... y'see... I thought negative numbers were 'smaller' than zero.

    No. Negativity simply donates direction. -9999999999999 is a very large (in magnitude) number
    Wouldn't 'minus infinity' be infinity's reciprocal?

    No.
    As for zero, the opposite of 'nothing' isn't necessarily 'everything'. It could merely be 'something'.

    I didnt say zero was the opposite of 'everything'.
    As ecksor said physical existence has nothing to do with it.

    To do with what?


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  • Moderators, Social & Fun Moderators Posts: 10,501 Mod ✭✭✭✭ecksor


    Physical existence has nothing to do with how an operation is defined (or not) on a particular set.

    But then, you seem to view the actual mathematics of this as irrelevant, which is odd since you also assert that infinity cannot physically exist.

    The question of whether 0 is the smallest number that can exist is actually an good example of how such things can be confusing. Bard claims that negative numbers are smaller, which is correct if you take a set such as the integers or the reals and the operation < (less than), but you then correct him and reveal that you're actually using a different set of goalposts (the set of natural numbers, or non-negative reals or some such, who knows).

    Anyway, I don't think this a useful discussion to continue.


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