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Whaaaat  Proof that 1 = 2

 Lemon Quarter
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 Lemon Pip
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 Lemon Quarter
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Re: Whaaaat  Proof that 1 = 2
SteelCamel wrote:Hmm...
Let a=b
then later
divide everything by ab
...and what is ab?
Yes the old "divide both sides by zero" thing that most 'proofs' that something = something else rely on, when it obviously doesn't!

 Lemon Quarter
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Re: Whaaaat  Proof that 1 = 2
and even forgetting the divide both sides by zero ... the euqation is already starding at 0=0 and thats it, game over
(a+b)(ab)=b(ab)
is (a+b) * 0 = b *0
0 =0
that's it.
as an exercise though it gets the students thinking about what they are really dealing with I guess! And allows the lecturer to explain that you cannot/do not/should not divide by zero
(a+b)(ab)=b(ab)
is (a+b) * 0 = b *0
0 =0
that's it.
as an exercise though it gets the students thinking about what they are really dealing with I guess! And allows the lecturer to explain that you cannot/do not/should not divide by zero

 Lemon Quarter
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Re: Whaaaat  Proof that 1 = 2
Errr ... did any of you actually watch the video all the way through?!? It's only 3 minutes long and at the end he does explain why it's nonsense.
Don't divide by zero or you'll end up proving this, and then nothing in the universe will make sense.
Don't divide by zero or you'll end up proving this, and then nothing in the universe will make sense.

 Lemon Half
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Re: Whaaaat  Proof that 1 = 2
Series to infinity  double each term
Z = 1 + 2 + 4 + 8 + 16 .......+ ∞
2Z = 2 + 4 + 8 + 16 ..... + ∞
Z  2Z = 1
Z= 1
so 1 + 2 + 4 + 8 + 16 .......+ ∞ = 1
Z = 1 + 2 + 4 + 8 + 16 .......+ ∞
2Z = 2 + 4 + 8 + 16 ..... + ∞
Z  2Z = 1
Z= 1
so 1 + 2 + 4 + 8 + 16 .......+ ∞ = 1

 Lemon Quarter
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Re: Whaaaat  Proof that 1 = 2
AleisterCrowley wrote:Series to infinity  double each term
Z = 1 + 2 + 4 + 8 + 16 .......+ ∞
2Z = 2 + 4 + 8 + 16 ..... + ∞
Z  2Z = 1
Z= 1
so 1 + 2 + 4 + 8 + 16 .......+ ∞ = 1
I think this mainly illustrates my old maths teacher was right when he maintained infinity is indeterminate rather than a value. Therefore like dividing by zero, it doesn't work in equations like this.

 Lemon Quarter
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Re: Whaaaat  Proof that 1 = 2
Mike4 wrote:AleisterCrowley wrote:Series to infinity  double each term
Z = 1 + 2 + 4 + 8 + 16 .......+ ∞
2Z = 2 + 4 + 8 + 16 ..... + ∞
Z  2Z = 1
Z= 1
so 1 + 2 + 4 + 8 + 16 .......+ ∞ = 1
I think this mainly illustrates my old maths teacher was right when he maintained infinity is indeterminate rather than a value. Therefore like dividing by zero, it doesn't work in equations like this.
It's actually rather more complicated than that. 'Infinity' is not a single mathematical concept, but many different concepts  and each of them has different rules about manipulating it. That particular proof breaks the rules about working with infinite sequences in the 'real numbers' (which are what we normally think of as just 'numbers'), for instance, but it is the essence of a valid proof in the '2adic integers' (see https://en.wikipedia.org/wiki/Padic_number if you want the gory details of what they are!), and that's related to the fact that computers generally represent 1 in "two's complement" form as a binary number in which all the bits are 1s.
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