Re: Fundamental Theorem of Arithmetic


"Mark Nudelman" <markn@xxxxxxxxxxxxxxxxxxxxx> wrote in message
news:CcSdnaHiW6AipyjYnZ2dnUVZ_o7inZ2d@xxxxxxxxxxxxxx
On 1/19/2007 5:58 AM, Nick wrote:
"Gerry Myerson" <gerry@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
news:gerry-82660D.09161919012007@xxxxxxxxxxxxxxxxxxxxx
In article <mMydnTPYMb5CHjLYnZ2dnUVZ8sSrnZ2d@xxxxxx>,
"Nick" <tulse04-news1@xxxxxxxxxxx> wrote:

I came across the Fundamental Theorem of Arithmetic - which I have
never
heard so called - it is also known as the Unique Factorization
Theorem -
again a term I have never heard.
So...what *have* you heard it called?

I have never heard it called anything. I took it for granted.

[snip]

PS My maths (in the UK) was not hung up on learning names of theorems. I
might add that often fundamental theorems are so fundamental that the
person doesn't bother thinking about them.

While the FTA may seem obvious, it really isn't. In fact, in some number
systems, it is false -- a number can have two different prime
factorizations. So it really is necessary to state it as a theorem and
prove it.

Going back to my textbook did show that I did have it down as a theorem -
but this was one of many in my Linear Algebra course in my first year at
university (see the book by Serge Lang) - as I say no special name was given
to it. That was my point.

I don't think you are right concerning the number system. My algebra course
and the theorem did not mention a specific number system.

Primes are primes independent of the number base.

64 has a square root of 8 - and 1000000 (binary) has a square root of 1000.

19 is prime (decimal) and so is its equivalent in binary - I would suggest.

If I divide by 5 (101 - binary) the answer is the same whether the
calculation is done in decimal or binary.

Nick


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