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Logical paradoxes or fallacies    Synchronic thinking    Multi-dimensional    Optical Illusion

Main references: Wikipedia's Paradoxes   Fallacy   Deductive fallacy Paradoxes and Contemporary Logic

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...... Logical paradoxes or fallacies ......

Moderately difficult Moderately difficult

Can 2=1 ?

If A=B
Multiply both sides by A, you get A²=AB.
Subtract B² from both sides, you get A²-B²=AB-B².
Factor both sides make it (A+B)(A-B)=B(A-B).
Divide both sides by (A-B), you get A+B=B.
Because A=B, therefore B+B=B,
If 2B=B, then 2=1.


Similar puzzle can also be seen at Math Puzzle (2=1).
This is the puzzle slightly modified from: Dime turns into a dollar

If you square $ 0.10 it equals to this $ 0.01.
$ (0.10)² = $ 0.01.
So you will get a penny

However if you square 10 cents you get 100 cents.
(10)² cents = 100 cents.
So you just earned a full dollar out of a dime

If you square $ 1 it equals to this $ 1.
$ 1² = $ 1.
So you will still get a dollar.

However if you square 100 cents you get 10000 cents.
(100)² cents = 10000 cents.
So you just earned a hundred dollars out of a dollar. Answer   Answer

Can 2=1 ?. Penny is bettwr than dollar.

Bird brain No-brainer
Logical fallacy
Source: Natural Born Conservative  (alt)--> Black and White
Logical fallacy
Source: INTRODUCTION TO LOGIC--> I think, Therefore I am.
Black and White Dogs = Cats

Good examples of logical fallacies can seen at these sites: Logic & Fallacies. Fallacies.
Good examples of logical paradoxes can seen at these sites:
Wikipedia's List of paradoxes.
Socratic paradox: "I know nothing at all."
Quine's paradox: "Never say 'never'"
Liar paradox : "This sentence is false."
Liar paradox: The fictional speaker Epimenides, a Cretan: "All Cretans are liars."
Logical fallacies. Logical paradoxes.

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