/sci/ - Science & Math

Ahem. a/b where a = 0 and b=/= 0.

how about 0/1?

Well, since I doubt 0 is a rational number, I also doubt that 0 is an integer. Can you tell me why is zero an integer?

>>2250042
This.

Also, 0 is fundamentally required to define certain sets of numbers.

>>2250041
Can you prove that?

>>2250049
.Can you prove that?.

obvious troll is obvious

Well, if zero was an irrational number, you could not say that it is an integer; and thus making you unable to write zero as a/b.

>>2250054

Learn2numbers and/or Learn2troll.

1 is an integer
the ring of integers is closed under subtraction
1 − 1 = 0
Therefore 0 is an integer
0 = 0 / 1
Therefore 0 is a rational number

>>2250059
Yeah, but can you prove that?

0 is an integer because we need an additive identity in the integers

>>2250062
I'm not convinced.

I am asking this question seriously. I mean if you can say "0=0/1 so it is a rational number" it becomes recursive.

How about: "sqrt(2)/1=sqrt(2), so it is a rational number"

>>2250039
0 = 0/1

\thread

>>2250062
the ring of integers is closed under subtraction BECAUSE people consider 0 an integer. It's like saying "0 is an integer because it is an integer." It does not make any sense, not even enough to convince me.

>>2250066
Nope, cause sqr(2) isnt an integer

How old are you?

>>2250075
oh look someone who has only taken calculus and has never heard of an axiom.

>>2250076
You don't have to resort to name calling. Just admit that you can't prove it.

>>2250075
>0 an integer

Yes, 0 is considered an Integer.....DURRR
wtf is your point?

Peano arithmetic starts with "blabla is a natural number". You can choose blabla arbitrarily, thus 0 is a natural number. You can change axioms at will, and if you don't create something different with that all the implications stay the same.

>>2250082
Thus you prove you don't get it.

You don't prove axioms, they are the rules to the game.

>>2250087
Why were you trying to prove 0 is an integer?

>>2250085
>>2250087

>>2250090
show me were in my two anonymous postings i was trying to prove anything.

>>2250090
Headshot. (But I guess the crank will continue anyway.)

I'm so glad I earned the right to be an elitist prick sometimes. I'll make use of this now by stating that I don't have the slightest interest to contribute to OP's knowledge and he can go fuck himself. Also, thread hidden.

Posting in gayest thread

Wtf. This thread is still alive.

OP go kill yourself.

first sub zero...

NOW PLAIN ZERO

EVERYONE CHILL THE FUCK OUT.

>>2250066

i don't think you understand how integers are defined.
the set of integers is DEFINED as a RING with identity 1. since it is a RING, it requires EXISTENCE AND UNIQUENESS of an additive identity, BY DEFINITION OF A RING.
ZERO, is DEFINED such that a+0 = a for any a in R.
since ZERO is an additive identity, ZERO is in the set of all integers.

now to show that ZERO is RATIONAL
To show that q is rational, you have to show that q can be expressed as a/b where a, b are integers.
we showed that ZERO is an INTEGER, and 1 is an INTEGER by DEFINITION
and since 0 = 0/1 (because (a-a)/1 = a - a = 0 because 1 is a MULTIPLICATIVE IDENTITY), 0 is a rational

>>2250327
0 is an integer by definition. thus it is a rational number since all integers are rational numbers. it also real, and complex. i don't see the problem. oh wait, I do: OP is gay.

>>2250343
That's racist.

>>2250350
your thread bumping is racist.