In my quest to discover why 1 is not a prime, I have found out that since the time of Euclid, 1 has not even been a number!?!
I am giving up. Not so much conceding defeat as loosing by default while I slouch away from this mad-hatter numerology, muttering and shaking my head. You see, the prime reason "One" can't be a prime number is that it isn't even a number to begin with.
This is more than my little pea brain (and I only have the 1, you see, so my number of brains is . . . well, not 0, since 1 is not zero, but it has to be zero because 1 is not a number - can you see where this is taking me?) can handle.
This is probably why I became a lowly chemist, whose approach to numbers (and/or units) is strictly utilitarian.
I am going to make me a unit of honking big martini, with a legitimate prime, odd and Fibonacci number of jumbo olives. (Three, if you must know.)
Cheers!
JzB who is one perplexed unit (if that's not redundant)
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Sunday December 22, 2024 Alan Massengill
15 hours ago
9 comments:
This is beginning to sound like republican trickle down economics.
Hmmmm.
There's a unit of difference though. The mathematicians might actually be right.
OTOH, trickle-down is pure bull shit.
Cheers!
JzB
well it's a divisor. For the prime factorization to work, though one's ...just one, yet all primes are numbers (and the prime algorithm works fine with one not being prime). Who said life was perfect? When the bridge holds, it holds, or if the tanks roll, they roll (metallurgy at least as critical as the mathematics)--regardless if some of the equations don't please all the ponderous platonic pedants in college town
ponderous platonic pedants
Hey that's better than "nattering nabobs of negativism!"
One as not prime could be assumed to be a mathematical given (but it does have to do with unique factorization).
What seems weirder is....that there are infinite prime numbers (as per Euclid), AND of course infinite rational numbers, or infinite even numbers, so forth--even tho at any given magnitude, the integers would greatly outnumber the primes. So does the infinity of primes equal the infinity of integers, or not? That seems quite odd...that there could be different sized infinities. That, or...reject the idea of numerical infinity itself --just another name for...very large. But infinities don't "exist" in the sense say the Ring nebula does--it only matters when counting. Or something like that.
Having infinities of different sizes troubles me not at all. There are an infinite number of points on a line, and infinity^2 points in a plane.
"One" not being a number (not even the loneliest) trouble me a lot.
My solution is to not think about it.
That same approach extended my membership in the Catholic Church by at least a decade.
Cheers!
JzB
well, that's what some math teachers say: not all. Infinite divisibility (merely being able to cut the pie endlessly) is NOT infinite magnitude (ie there's no actual inf. between one and two, or one and one million, even tho' some naive math. people want you to think so). And it is an issue for math students, having to do with cardinality, and other fun stuff (and probably one reason why they put Cantor in a madhouse). While it would take some work to prove it...Finitism holds (infinity being about countability, and merely potential. Not an actual "thing").
Anyway, one does not meet the accepted definition of prime #s; ie divisible by exactly two numbers, and only two--ONE and itself. It's divisible only by one. So at least no logical equivalence.
I would say that infinity and infinity^2 are the same number...infinity, same as the number of points between 1 and 2.
And infinity is a definite point. After all, you can integrate from, say, 0 to infinity and get a real solution.
JC -
Well, I guess you can integrate from 1 to infinity, but the segregationists will always be with us.
J -
Your last point takes me back to where I started: 1 is the degenerate case, since "1" and "itself" are the same.
Anyway, I'm slouching away from all this, and going back to economics, where you can just make shit up, and Euclid won't care.
Cheers!
JzB
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