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Subject: "spurious math"     Previous Topic | Next Topic
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alexbadmin
Charter Member
1866 posts
Jul-24-06, 06:48 AM (EST)
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"spurious math"
 
   I have recently come across a shallow equality with a deep appearance and little sense:

[e][π] + [π] = [π][e] + [e]


I'd be grateful for more examples.

Thank you,
Alex


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mr_homm
Member since May-22-05
Jul-24-06, 00:05 AM (EST)
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1. "RE: spurious math"
In response to message #0
 
   Well, there's the fake "proof by example" that square root is linear:

[sqrt(2)] + [sqrt(2)] = [sqrt(4)]
[sqrt(3)] + [sqrt(3)] = [sqrt(6)]
[sqrt(8)] + [sqrt(8)] = [sqrt(16)]

This works the same way as your example, by using the greatest integer operation to change the apparent value to something trivial.

Here's another:

Let I be the iteration operator, so that I(o,n) iterates the operation o n times. For an arbitrary ring G and a in G, let a+ be left addition by a and a* be left multiplication by a.

Theorem: For the real number field, there is a unique element a for which for which the additive and multiplicative operations coincide, i.e., I(a+,1)(a) = I(a*,1)(a).

Proof:

2+2 = 4 = 2*2.

QED

I just made this last one up on the spot. Hope it's amusing.

Stuart Anderson


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alexbadmin
Charter Member
1866 posts
Jul-25-06, 00:06 AM (EST)
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2. "RE: spurious math"
In response to message #1
 
   Very good. Thank you.


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