A paradox is a statement that apparently contradicts itself and yet might be true. Most logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking.
Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined.
In common usage, the word "paradox" often refers to statements that are ironic or unexpected, such as "the paradox that standing is more tiring than walking".
A fallacy is the use of poor, or invalid reasoning for the construction of an argument. It is also used to refer to "an argument which appears to be correct but is not."[3] If an argument is fallacious it does not necessarily mean the conclusion is false.
Some fallacies are committed intentionally (to manipulate or persuade by deception), others unintentionally due to carelessness or ignorance. (Wikipedia)
If A=B
Multiply by A on both sides, you get A²=AB.
Subtract B² from both sides,
you get A²-B²=AB-B².
Factor both sides, you get (A+B)(A-B)=B(A-B).
Divide by (A-B) on both sides, you get A+B=B.
Because A=B, therefore B+B=B,
If 2B=B, then 2=1.
Answer: The problem is when you try to divide both sides by (A-B).
Because A=B, therefore (A-B)=0.
You can't divide any equation by zero.
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
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We know that if you square 0.01 meter, you get (0.01 m)² which is 0.0001 m² and
if you square 10 centimeters, you get (10 cm)² which is 100 cm².
An area of 0.0001 m² is exactly the same as an area of 100 cm². So far so good.
However, if you want to square $ 0.1, you will get ($ 0.1)² which should be $² 0.01 and
if you want to square 10 cents, you will get (10 cents)² which should be 100 cents²
There is no such thing as $² or cents².
On the other hand, you can argue it this way.
Since $ 1= 100 cents, then ($)² wil equal (100 cents)² which should be 10000 cents².
In this case, 0.01 $² will equal 0.01 X 10000 cents² which is 100 cents².
Good examples of logical fallacies can seen at these sites:
www.infidels.org: Logic & Fallacies.
www.nizkor.org: 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."
