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/sci/ - Science & Math

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6527109 No.6527109[DELETED]  [Reply] [Original]

Lets all agree that 2 is not a prime.

>> No.6527124

>>6527109

Except it is. The only natural multiples of 2 are itself and 1. Ergo, it is prime.

>> No.6527136

>>6527109
I don't deny that 2 not being a prime would make some results a lot easier to deal with lol.

>> No.6527166

It cannot be a prime because it's even.

>> No.6527197

>>6527166
That's like saying 3 cannot be a prime because it's divisible by 3.

>> No.6527214

>>6527166
all squares are fags but not all fags are squares

>> No.6527279

>>6527109
I'm in, it's a shitty prime anyway.

>> No.6527297

>>6527214
I don't see the relevance of this analogy.

>> No.6527298

>>6527109
if 2 isnt a prime does that make 4 a prime?

>> No.6527302

>>6527298
No, but it does make 3 even.

>> No.6527305

>>6527297
I have a higher IQ than you so I will not explain the relevance of it to you.

>> No.6527306

>>6527197
evenness is highly nontrivial! We define evenness recursively such that if n = 0, n is even, or n-1 is odd. And we define oddness to be n = 1, or n-1 is even.

>> No.6527354

I'm not sure what's going on in this thread.

>> No.6527391

>>6527306
Why would you even do that?
n is even <-> there is a k such that 2k = n
n is odd <-> n is not even
there you have it

>> No.6527392

>>6527109
yeah, so prime decomposition will be fucked up and consequently all of number theory.
Good idea OP

>> No.6527393

Let's all agree that 7 is not a number. Fuck 7.

>> No.6527438

If 2 isn't prime, then if we do prime factorization of 4, we can't get 2, so the factors must be only 1 and 4. 4 is now prime. Proof by contradiction.

>> No.6527779

>>6527438
No, silly, no even numbers are prime.

>> No.6527787

>>6527779
If 2 isn't prime, why should 3 be prime? To say that no even numbers are prime doesn't make any more sense than saying no multiples of 3 are prime. Any non-retard will recognize that that one prime number is even, one is a multiple of 3, etc.

>> No.6527854

but if 2 were not prime then there would be a natural without a prime power factorization that was not the empty product

>> No.6527887

SOURCE!!!!!!!!!!!!!!!!!!!!!!!

>> No.6527891

>>6527779
I MEAN YOU MOTHERFUCKER!!!!!!!!!!!!!!!

>> No.6527922

>>6527109
>Lets all agree that 2 is not a prime.
Then the Fundamental Theorem of Arithmetic is broken. Number theory has become meaningless, and math has fallen apart. Congratulations, you're retarded.

>> No.6527931

>>6527787
It's only divisible by 1 and itself, and isn't even. Come on man, are you paying attention?

>> No.6527942

5 isn't prime either. Because it's divisible by 5 and no other numbers that are divisible by five are prime. Why would we make an exception for just one number which is divisible by 5?

5/10, made me reply.

>> No.6527952
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6527952

Definition: A natural number (i.e. 1, 2, 3, 4, 5, 6, etc.) is called a prime or a prime number if it has exactly two positive divisors, 1 and the number itself.

The number 2 is prime but the number 1 is excluded to uphold the fundamental theorem of arithmetic.

en.wikipedia.org/wiki/Prime_number

>> No.6527953

>>6527952
>arbitrarily exclude some number
>but don't arbitrarily exclude some other number
this is what passes for math

>> No.6527957

>>6527953
It's not arbitrary. 1^n=1 if n=/=0 so it does not fit the definition.

>> No.6527959
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6527959

>>6527957
>THE definition
was it on the back of the ten commandments?

>> No.6527962

>>6527953
n is product over finite multiset of primes
1 is the product of the empty set

>> No.6527973

>>6527953
> >arbitrarily exclude
The number 2 has two factors.
The number 1 has one factor.

Prime numbers are those numbers that have two factors.

Ergo, 2 is prime, and 1 is not prime.

>> No.6527974

>>6527959
We choose to define primes that way because it is useful.

We could have a separate definition which is that the number of divisors is less than two for it to be prime. Then 1 is included and the fundamental theorem needs to be heavily modified in a way such that 1 is eventually excluded from being prime again. It works. Trust me. Smarter people than you know that there is no arbitrary decision here.

>> No.6527977

>>6527974
I don't think you know what the word arbitrary means.

>> No.6527978

>>6527973
1 is divisible by 0

>> No.6527984

>>6527978
>1 is divisible by 0
There is no natural number that, when multiplied by 0, gives 1.
If this is bait, it's -1/10.

>> No.6527985

>>6527977
I think he does.

>> No.6527988

>>6527984
there's no number that's the square root of -1 but that didn't stop mathematicians from defining it as i

let us define j
j*0 = 1

>> No.6527993

>>6527977
I do. I'm saying the definition is based on a fundamental property and not an arbitrary decision.

>> No.6527997

>>6527988
#Rekt.

>> No.6527999

>>6527993
Was the establishment of this fundamental property an arbitrary decision, or did it arise out of another fundamental property?

>> No.6528001

>>6527977
What do you think it means?

>> No.6528003

>>6527988
>there's no number that's the square root of -1
There IS a number that, when squared, gives -1. However, it's not a real number. So there is no real number whose square is -1 (but there are two imaginary solutions).

>let us define j
>j*0 = 1
There is no number, real or imaginary or complex or quaternion, that satisfies this condition, dumbass.

>> No.6528014

>>6527999
all of math stems from a few chosen axioms.

the choice of axiom is not entirely arbitrary as we want these axioms to produce such well structures as, for example, the natural numbers.

>> No.6528016

>>6528003
If you don't see how his proposition is equivalent to the establishment of i, you're the troglodyte here.

Once upon a time there was no such thing as an "imaginary number" solely because all imaginary numbers relate to i. He has just established a j-class number, in the same way i-class numbers, now colloquially called "imaginary" numbers, were once established.

TL;DR, there is now a number that, when multiplied by 0, gives 1. It's called j. How are you going to deal with it?

>> No.6528019

>>6527988
I would like to see you append that j to the real numbers without the arithmetic/algebraic structure collapsing in on itself.

>> No.6528022

>>6528016
Not the anon you are arguing with, but it is different as it doesn't lead to complex or useful structures.

That complexity or usefulness is not arbitrary.

>> No.6528023

>>6528019
Renee Descartes once thought imaginary numbers were a load of shit, too. Why does anyone here care what someone lesser than him thinks about j?

>> No.6528026

>>6528023
Well, a whole load of people greater than him think it isn't shit, also it turned out to be useful.

Also Descartes thought he could prove God. exists

>> No.6528038

>>6528023
People would never have argued for i had it not had some use or structure behind it. Moreover stop this "greater minds disagreed" argument from authority shite.

there's no advantage demonstrated by creating a j such that j*0 = 1. It's useless in arithmetic, you can't even use it in a ring because otherwise it would make 0=1

>> No.6528039

>>6528016
Oh god here we go.

The set of complex numbers arises naturally as the algebraic completion of the set of real numbers. The complex numbers "existed" as soon as the real numbers "existed". They weren't invented, they were discovered.

Calling the number i an arbitrary definition is pretty much the same as calling the number 1 an arbitrary definition. Learn some actual math before posting.

>there is now a number that, when multiplied by 0, gives 1.
Then we would have to completely change our definition of the real number system. The complex numbers, on the other hand, arise as an algebraic completion of the real numbers.

>> No.6528046

>obvious troll thread

>> No.6528068

>>6528039
And let me guess, according to you, divergent series can't equal anything other than plus or minus infinity.

Shut up, kid.

>> No.6528084

>>6527306
I've always seen evenness defined as 'n is even iff there exists an integer k such that n = 2k' which is equivalent to 'n is even iff 2|n'.

>> No.6528093

>>6527109
If 2 isn't a prime, what are the prime factors of 14?

>BOOM HEADSHOT.

>> No.6528102

>>6528068
>putting words in my mouth
Divergent series have a "traditional" value, and a "special value", which can be obtained through Ramanujan summation, zeta function regularization, etc. The "special sum" is used in physics and has interesting mathematical properties, but a divergent series has no traditionally well-defined value.

Go take your YouTube-tier math knowledge somewhere else.

>> No.6528109

>>6528046
It's only trolling autists. Most of us are just having fun.

>> No.6528142

>>6528102
Exactly. People defined different rules to suit their purposes. That's what maths is about.

Are you an engineer by any chance? I'd be surprised if you ever studied maths given your lack of perspective and low capacity for abstract thought.

>> No.6528214

>>6528093
It's official: 14 is now a prime number.

>> No.6528236

>>6528003

>let us define j
>j*0 = 1

And now whatever we defined j on is no longer a field

>> No.6528249

>>6528236
it's not even a ring

>> No.6528251

>>6528249
It's fucking nothing.

>> No.6528368

>>6528251
It's called nonassociative algebra. Most algebras aren't groups, rings, or fields. Learn some algebra yo.

>> No.6528458

>>6527214
>all squares are fags but not all fags are squares
jesus fuck just grow up, there's a word adults use to express this concept, it's called SUBSET

>> No.6528521

Is 1 prime?

>> No.6528525

>>6528521
>Is 1 prime?
Nope.

>> No.6528528

>>6528214
Nope, has a prime factor of 7. Try again!

>> No.6528547

>>6528458
That wasn't my point but ok

>> No.6529385

>>6527988
>engineering intensifies

>> No.6529392

>>6528528
14 has factors 1,7.

There was once thought to be a 3rd factor but it has been lost to us.

>> No.6529395

>>6529392
14 was once thought to be the only non square with an odd number of factors

>> No.6529422

>>6528093
2 is no longer prime, but all the other even numbers are now prime.

>> No.6529452

is the prime distribution fractal?

>> No.6529485

>>6527988
as long as you find a set containing both the real numbers and j, with an interesting structure (ring, field ...), you just made a discovery/creation as great as the complex numbers

>> No.6529489

>>6527109
so 4 is a prime because the only prime that divides it is 4?
and 8 is fucked up because it is divisible by the prime 4, but leaves a non-prime. does that make 8 a prime aswell because it cannot be factorized into other primes?

>> No.6529490

>>6529395
I'm confused.
14 has 2 prime factors.

>> No.6529491

>>6529489
rekt