Or just talk about the electric Universe.
Or just talk about the electric Universe.
I haven't read that thread but I have strong views on whether 1=0.9999999...
OMG I forgot all about that thread. Usually people only get that emotional when it involves quantum mechanics or silly putty. Or maybe invisible elves in the backyard, or maybe the size of a lepton, or perhaps the health benefits of laughing.
When I first heard hear there was a kerfuffle (yes that is an actual word) over the number one, I was as interested in that as most people are when I try to discuss the C_{37} alkenone distributions in the deep ocean core MD952011.
It is a theorem in the standard semantics of number theory, so yes. I'm also sure that this is not the right thread to discuss it, although you're of course free to start one - there is a special ATM section for such threads with its own rules, and let's be honest here, that would be about as ATM as it gets .
My understanding is that it is more than just convention. There is a class of operation * that works with Prime numbers ... except 1. It made more sense to exclude 1 from "being a Prime", than it did to add "... except 1" to that class of operation. Maybe you'd call that convention, but it is about the definition of these things.
(* I forgot what, so I checked Wikipedia: http://en.wikipedia.org/wiki/Prime_n...imality_of_one
)...
The crucial importance of prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic, which states that every integer larger than 1 can be written as a product of one or more primes in a way that is unique except for the order of the prime factors.[2] Primes can thus be considered the “basic building blocks” of the natural numbers.
...
Although a large body of mathematical work would still be valid when calling 1 a prime, the above fundamental theorem of arithmetic would not hold as stated. For example, the number 15 can be factored as 3 · 5 or 1 · 3 · 5. If 1 were admitted as a prime, these two presentations would be considered different factorizations of 15 into prime numbers, so the statement of that theorem would have to be modified
...
One thread herein: http://cosmoquest.org/forum/showthre...t-not-1-2-or-3
Last edited by pzkpfw; 2014-Jul-02 at 01:07 AM. Reason: Add to quote for clarity
Measure once, cut twice. Practice makes perfect.
Yes, that's why they adopted that convention - so you wouldn't have to add "except 1" to the fundamental theorem of arithmetic (as well as some others). Just because it has a reason doesn't mean it's not a convention, it just means it's a thought-out one.
But the other one isn't about definition, arguing that one would literally amount to stating . I suppose you could make it about definition by claiming something equivalent to "but when i write the squigles that make up '0.9...' i'm actually writing 42", but that's just silly.Maybe you'd call that convention, but it is about the definition of these things.
Think of the difference like this: if it's a convention then using the other way to do it in a mathematical theory would not necessarily mean that it's internally inconsistent. If it's not a convention then it would be (in this case because equality is probably the most basic operation necessary for pretty much all mathematics, and equality is reflexive).
I'm going to make the obvious leap and say that I have 0.99999999999999~ banned friends.
"I'm planning to live forever. So far, that's working perfectly." Steven Wright
I have a friend who is an invisible elf. Since he could not prove he existed, he was banned.
...I can't think of anything for Silly Putty.
"I'm planning to live forever. So far, that's working perfectly." Steven Wright
- The African coelacanth genome provides insights into tetrapod evolution
Count Basie has the most band friends.
"I'm planning to live forever. So far, that's working perfectly." Steven Wright
I need a band aid to win this.