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I stubled across 3 false proofs, see if you can find the errors. |
I stubled across 3 false proofs, see if you can find the errors. |
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+ | ==#1== |
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− | 1. |
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− | X=Y |
+ | * X=Y |
− | X^2=X*Y |
+ | * X^2=X*Y |
− | X^2-Y^2=X*Y-Y^2 |
+ | * X^2-Y^2=X*Y-Y^2 |
− | (X+Y)*(X-Y)=Y*(X-Y) |
+ | * (X+Y)*(X-Y)=Y*(X-Y) |
− | X+Y=Y |
+ | * X+Y=Y |
− | 2Y=Y |
+ | * 2Y=Y |
− | 2=1 |
+ | *2=1 |
+ | ==#2== |
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− | 2. |
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− | X=0.99999... |
+ | * X=0.99999... |
− | 10X=9.99999... |
+ | * 10X=9.99999... |
− | 10X-X=9.99999...-X |
+ | * 10X-X=9.99999...-X |
− | 9X=9 |
+ | * 9X=9 |
− | X=1 |
+ | *X=1 |
− | 0.99999...=1 |
+ | * 0.99999...=1 |
+ | ==#3== |
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− | 3. |
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This one is a word problem. |
This one is a word problem. |
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Imagine a square with sides of 4, and therefore a perimiter of 16. |
Imagine a square with sides of 4, and therefore a perimiter of 16. |
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− | Cut corners, and the perimiter stays the same |
+ | Cut corners, and the perimiter stays the same. See below for a visual. |
+ | ---- |
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− | Ex. |
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− | _____ ___ |
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− | | | equals _| |_ |
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− | | | |_ _| |
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− | |_____| |___| |
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+ | *HHHHHHHHHH |
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+ | *HHHHHHHHHH |
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+ | *HHHHHHHHHH |
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+ | *HHHHHHHHHH |
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+ | *HHHHHHHHHH |
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+ | *HHHHHHHHHH |
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+ | |||
+ | |||
+ | The perimeter of the above shape is equal to the perimeter of the shape below. |
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+ | (_ equals negative space) |
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+ | |||
+ | *____HHHH____ |
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+ | *____HHHH____ |
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+ | *HHHHHHHHHH |
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+ | *HHHHHHHHHH |
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+ | *____HHHH____ |
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+ | *____HHHH____ |
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+ | |||
+ | ---- |
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Repeat to infinity. |
Repeat to infinity. |
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Square becomes a circle |
Square becomes a circle |
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− | 16=Pi*(2)^2 |
+ | * 16=Pi*(2)^2 |
Therefore, Pi equals 4 |
Therefore, Pi equals 4 |
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+ | ---- |
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− | |||
That's all folks! |
That's all folks! |
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+ | ''~₮iger~'' :. [[User_talk:Keo5|<small>''Talk''</small>]] ''&'' [[User:Keo5|<small>''Profile''</small>]] .: |
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− | |||
[[Category:Blog posts]] |
[[Category:Blog posts]] |
Latest revision as of 23:01, 24 December 2011
I stubled across 3 false proofs, see if you can find the errors.
#1
- X=Y
- X^2=X*Y
- X^2-Y^2=X*Y-Y^2
- (X+Y)*(X-Y)=Y*(X-Y)
- X+Y=Y
- 2Y=Y
- 2=1
#2
- X=0.99999...
- 10X=9.99999...
- 10X-X=9.99999...-X
- 9X=9
- X=1
- 0.99999...=1
#3
This one is a word problem. Imagine a square with sides of 4, and therefore a perimiter of 16. Cut corners, and the perimiter stays the same. See below for a visual.
- HHHHHHHHHH
- HHHHHHHHHH
- HHHHHHHHHH
- HHHHHHHHHH
- HHHHHHHHHH
- HHHHHHHHHH
The perimeter of the above shape is equal to the perimeter of the shape below.
(_ equals negative space)
- ____HHHH____
- ____HHHH____
- HHHHHHHHHH
- HHHHHHHHHH
- ____HHHH____
- ____HHHH____
Repeat to infinity. Square becomes a circle
- 16=Pi*(2)^2
Therefore, Pi equals 4
That's all folks!