Truth, Lies, and Drinking Games OT

[olivierfouquet2000]

> << "Clang" for each prime number
> "Pow" for perfect squares
> "Zap" for powers of two
> Thus 1, 2, 3, 4 would be expressed as "Clang Pow", "Clang Zap",
> "Oink Clang", "Pow Zap". >>
> 
> Is 1 a perfect square? I've heard that 1 has been declared to be not a
> prime, because if it were a prime, it would be an exception to some
> Theorems about primes.
> 
> David wrote in http://groups.yahoo.com/group/the_old_crowd/message/1560 :
> 
> << Error. 1 is "Pow zap". >>
> 
> Is 2-to-the-0 a power of two?

Olivier
I cannot refrain myself from opening my big mouth anymore!
Being a mathematician and a number theorist to boot, I can give you a 100% safe answer 
on these, and also on one-sided black sheep.

Sooooooooooo

1 is a perfect square, 1 is a power of two and 1 is not a prime number.

1 is a perfect square because it is one squared (!). 

1 is a power of true because, well it is really a question of definition, but there is no 
reason to arbitrarily exclude zero from the other natural numbers, so yes it is two to the 
zero power.

1 is not a prime number because if so, the so-called fundamental theorem of arithmetics 
would be wrong, which is bad for a fundamental theorem. The theorem says that any 
natural number greater than 2 can be writtten in an unique way as a an unordered product 
of prime numbers. The key words here are "in an unique way." If 1 was a prime number, 
you could write 6 as 2 times 3 or 1 times 2 times 3 or 1 times 1 times 2 times 3 and that 
would lead to enormous problems.

In fact, failure to notice this fact probably lead Fermat to believe he had a proof of his 
celebrated last theorem, so that he scribbled some words about a margin being not wide 
enough, and the rest is history.

I promise this is the first and last post here about numbers

Olivier

PS: And of course, the most we can say about the sheep, is that it appears black on at least 
one side when seen from a train.