Tagged Questions
18
votes
4answers
1k views
Seems that I just proved $2=4$.
Solving $x^{x^{x^{.^{.^.}}}}=2\Rightarrow x^2=2\Rightarrow x=\sqrt 2$.
Solving $x^{x^{x^{.^{.^.}}}}=4\Rightarrow x^4=4\Rightarrow x=\sqrt 2$.
Therefore, $\sqrt 2^{\sqrt 2^{\sqrt 2^{.^{.^.}}}}=2$ and ...
9
votes
4answers
760 views
Two paradoxes: $\pi = 2$ and $\sqrt 2 = 2$ [duplicate]
Possible Duplicate:
Is value of $\pi = 4$?
Can anyone explain how to properly resolve two paradoxes in this YouTube video by James Tanton?
2
votes
2answers
239 views
An unwanted property of the set $T=\{x,\{x\} \}$
Let $T$ be $T=\{x,\{x\},y \}$ and let $f:A\rightarrow T, \ f(a):=x$, where $A=\{a\}$. Define $B=\{x,y \}$. Now a weird thing happens: We should have that $x \in f(f^{-1}(B))$ by construciton of $f$, ...
1
vote
5answers
486 views
How to explain this paradox involving coin-tosses?
I do this experiment:
I flip fair coin, if it comes heads on first toss I win.
If it comes tails, I flip it two times more and if both heads I win.
Else, I flip it 3 more times, if it comes heads all ...
38
votes
7answers
4k views
Infinity = -1 paradox
I puzzled two high school Pre-calc math teachers today with a little proof (maybe not) I found a couple years ago that infinity is equal to -1:
Let x equal the geometric series: $1 + 2 + 4 + 8 + 16 ...
