
Possibly the
greatest paradox is that mathematics has paradoxes...




















Paradox
of wizard and mermaid





Paradox
of rich wizard and mermaid is a
paradox involving infinities. It
can be seen as an example that is
undefined operation. Playing around
undefined operation it is possible
to get any wanted result. 
An
infinitely rich wizard has a mermaid
in the pond of his garden. He likes
to play with her and gold coins. Every
minute he throws two coins in the pond
and she throws him back one coin after
a half minute.
When
this game is allowed to run forever,
how will the money be distributed? We
are allowed put a label on all the coins,
numbering them 1,2,3,4, etc.
Solution
1 
The wizard
gives the mermaid coin number
1 and 2, she returns number
1. He gives her number 3 and
4, she returns number 2. He
gives her number 5 and 6, she
returns number 3. And so forth.
Conclusion: eventually
each coin returns to the wizard,
so he will have everything back
again and she has nothing.

Solution
2 
The
wizard gives the mermaid coin
number 1 and 2, she returns
number 2, keeping number 1.
He gives her number 2 again
together with 3, she returns
number 3, keeping number 2.
He throws number 3 and 4 in
the pond, she gives him number
4 back, keeping number 3. And
so forth.
Conclusion: at the end
she will keep all the coins,
and the wizard has nothing.

Solution
3 
The
wizard gives the mermaid coin
number 1 and 2, she returns
number 2, keeping number 1.
Next time, however, the wizard
throws coin number 3 and 4 in
the pond, the mermaid keeping
number 3, returning number 4.
And so forth.
Conclusion: at the end
she will have all the odd numbered
coins and the wizard all the
even numbered, so both are equally
rich.

by
Tetyana Butler






Complex
analysis is studying the most unexpected, surprising,
even paradoxical ideas in mathematics. The familiar
rules of algebra and trigonometry of real numbers
may break down when applied to complex numbers.
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