/sci/ - Science & Math

I can if we assume zero exists.
I cant if we don't.

Dunno op. You can try reading Principa Matematica, i dont want to spoof 30 pages of that

>>10568949
cmon anon this one's easy
2 = 2 * 1 = 1 + 1
^:)

>>10568949
a thing plus another thing = 2 things

Well anon. If you have one apple, and I give you one more apple, you will have two apples total!

>>10568954
It's only a few lines iir. Define a set with addition operator and 0 into existence, closed on addition, 0+x=x, and with an element 1 which is 1+x=1 => x=0. Then you have a set where each element is ordered and equal to the addition of a number of 1s and the first element after 1 in that order (use symbol 2 for it) will be 1+1=2.

>>10569027
Now what if I wanted to share one apple equally among zero people?

>>10569069
Take the limit of sharing an apple among x people as x goes to 0.

Language, mathematics only works to communicate a point by assigning and dezignatic meaning to certain expressions-symbols. Meaning if I draw the symbol 1 and assign it tue meaning of representing a single item and then assign a meaning to sybol 2 as representing two items or two symbols of the item... Language and communication aka relativity are posible only by intention and symbolism. So if I say it does, it does and if you think it does not then it does not!

>>10569072
Goddamnit we dont have time for this Leroy! That table of 0 people is outside of this kitchen right now sitting in the VIP section and they've been waiting over 30 minutes for their order! We cant handle another bad Yelp review so give me an answer NOW!

>>10569072
That limit doesn't exist, brainlet.

>>10568964
you, sir, are a prime example of our species /)

>>10569101
>dezignatic
What?

>>10569101
>if I say it does, it does and if you think it does not then it does not!
That's a contradiction

>>10568949
Follow the rules and you will win a prize:
1) one is a number
2) one is a number (same as rule 1)
3) one *and* one is one *and* one
4) one *and* one is two

>>10568949

>>10568964
Bingo

>>10568949
let
0 = {}
and
1 = {{}}
and
2 = {{{}}, {}}
and so on...

Let A be a set.
Let Predecessor(1) = Predecessor({{}}) = 0.
Let Successor(0) = Successor({}) = {{}} = 1.
Let Successor(1) = Successor({{}}) = {{{}},{}} = 2.
Let Predecessor(A + 1) = A
Let Successor(A) = A + 1
Let Predecessor[Successor(A)] = A

1 + 1 = {} + 1 = Successor(A) = 2.

QED?

>>10569775
Why not just let 1 + 1 = 2?

>>10568949 (OP)
let
0 = {}
and
1 = {{}}
and
2 = {{{}}, {}}
and so on...

Let A be a set.
Let Predecessor(1) = Predecessor({{}}) = 0.
Let Successor(0) = Successor({}) = {{}} = 1.
Let Successor(1) = Successor({{}}) = {{{}},{}} = 2.
Let Predecessor(A + 1) = A
Let Successor(A) = A + 1
Let Predecessor[Successor(A)] = A

1 + 1 = {{}} + 1 = Successor(1) = 2.

QED?

>>10569183
He's saying it's subjective. Because it is. It's just symbols made by us to represent something that someone said it should represent.

Assume
1 + 1 = x and x != 2

By the additive inverse property of the number one we find
1 = x - 1

Here we invoke a contradiction because the only such x is 2.

>>10569775
>Let
Let's not

>>10569781
You can do that
But from that rule, what is 1 + 2..or 1+3, or 2+2....it's just not as interesting if you do it that way.

>>10569784
this gives explicit instructions on how "+" acts on whole number.

>>10569789
>because the only such x is 2.
Prove it

>>10569789
What this "+" symbol? What does it do?

What does "1" mean, What does "2" mean?

>>10569226
Based Coqposter

>>10569736
Whos dis semen demon?

Easy.

>>10569129
? it's infinity

>>10568949
Try this experiment anon.
Take one apple, put it on the table, then take one more and put it next to it. Then count the apples.
If they are 2, there's your proof.
Try it as many times as you want it will always be two.
Now there are 2 possibilities.
Either I am a wizard with mysterious powers, or you are a faggot.
Pick one.

>>10570414
What definition of limit are we working with?

>>10570434
I'm gonna go with option 2, OP is a massive faggot and should delete this thread immediately.

>>10570113
seconded

>>10570401
This is the best explanation I've seen so far

1 + 1 = 2
1 + 1 - 1 = 2 - 1
1 = 1

Prove that a set contains the elements it contains

[math]2^0 × 2 = 2[/math]

>>10570581
By definition of contains, QED

>>10570604
>QED
Cringe

I just work in an axiomatic system where its true

>>10569784
This is the correct answer.

>>10570635
t. brainlet

>>10570607
What, you draw a box like an illiterate fuck?

>>10570686
How does adding an extra symbol at the end of a proof help in any way?

>>10569798
Two, as the second natural number, is endowed with the property that it is one greater than the first natural number. The first natural number is one so
2 - 1 = 0

Suppose there is some other number with this property besides the second element of the natural numbers. Then
2 - 1 = x - 1

By the additive inverse property of the number one we obtain
2 = x

which contradicts our supposition that x != 2

>>10569789
Nice high school proof

Let the axiom of addition be that for all [math]x,y\in R x+y=x+y[/math]
1+1=2
QED

{} = 0
{0} = 1
{1} = 2
1+1={0}+{0}={1}=2

>>10570735
>2 - 1 = 0
2-1 = 1 ≠ 0

>>10570799
Not a proof

>>10569784
Autistic but correct.

>>10570787
I actually like what anon was doing (c.p.
>10570735). Of course most people that have any idea about math will provide the typical Peano Arithmetic style proof by recursion. The proof relying on uniqueness of inverses is somewhat unusal, but interesting in that it relies on a general property of rings (namely the uniqueness of inverses).

>>10570434
Absolutely retarded

>>10570909
Retard

>>10570909
>Not a proof
It's literally a proof you mouth breathing trog. No one ever said what axioms were allowed.

>>10568949
Hey guy, hey hey hey. Huehuehue, prove an assumption, hurr, durr, me so smart

>>10570952
It not an assumption, its a result of set theory. Although if it were an assumption, it indeed wouldnt be provable.

>>10570922
Generally people assume conventional axioms and definitions, provided they exist, and x+y=x+y is certainly not a standard axiom of integer arithmetic. Of course it could be - although its not really necessary. Perhaps you're thinking of the communtativity of addition, which states that x+y=y+x? In that case it could be a proof, but usually we'd be looking for something a more so implicit in the definition and axioms. Basically, you take the definition and axioms for additive identity, the definition and axioms for addition operator, and a set of constant terms (numerals) that denote ordinal positions of numbers in the integer sequence, and from that you can prove that by the definition and axioms of the + operator (which is a function taking two arguments) and the values of the constants 1, 2 you can prove that 1+1=2 without assumimg by definition that the formulae "1+1" and "2" mean the same thing in your model.

>>10571060
Let 1 + 1 = 2. QED.

>>10571133
2/8

>Fermats Last Theorem
>Proof: Let a^3 + b^3 != c^3 for all integers a, b, c. Q.E.D.

>>10568949
didn't newton do this in principia?

>>10571060
>>10571146
Not everyone defines "1 + 1 = 2" as representing a statement about naturals numbers constructed in set theory in von neumann style, brainlet. This >>10569784 excuse of a "proof" is pathetic.
>hurr durr the proof must define "1 + 1 = 2" in axiomatic systems that I have in mind but have not told anyone.
Also,
>It not an assumption
It is an assumption using the peano axioms, but is that also an axiomatic system not allowed since it was not the one you have in mind?

>>10570882
What dose "+" do?

>>10571166
I don't know, OP used it in his post, so he must, otherwise he's just posting a meaningless string of characters

>>10571166
I don't know, OP used it in his post, so he must know. Otherwise, he's just asking us to prove a meaningless string of characters

>>10571172
Tuche

>>10571161
What else would someone interpret the formula "1 + 1 = 2" as? There is no other standardized intepretation for these symbols other than modular groups of integers, and in that case it would have been prudent to explicitly state that we were working modulo some integer.

Of course you can use the set of symbols {1, 2, +, =} in some completely unrelated L-structure, but thats retarded and nobody ever does so.

>>10571190
How can you even get that "1 + 1 = 2" is about the group of integers (that is, knowing it is a group), without knowing that 1 + 1 = 2?

>>10568949
Well, we know, as an obscure result from barnett integration that 1 +2 +3 +4 +... = -1/12
So what you are going to want to do is move the 2 and -1/12 to the other sides so you get
1/12 +1 +3 +4 ... = -2
Now multiply by -1
-1/12 -1 -3 -4 -5... = 2
Now put LHS in a common fraction and factor out the ones
(-1)(1+12+36+48+...) = 2
Using the fact that 12+36+48+... is 12* the original series
(-1)(1 +-1/12*12)=-1*(1+1)=2
Dropping the negative,
1+1 = 2
QED

Assume there is a stick of lenght 2, and a point A located in the middle of such a stick. If the stick is snapped at point A the lenght of the two separate halves are 1. Therefore if these halves were put together, their lenght would be 2. Therefore 1 + 1=2.

>>10571392
That is scientific experimenr, not a mathematical proof.

>>10571327
Okay whatever, but I do hope you at least realize the circular logic in this.

>>10568949
Gib Peano axioms first

>>10571327
barnetts work is flawed
he states that 0+1+2+3+... is -1/12
but the sum 0+1+2+3+... is trivially shown to be 5/12

>>10572437
That's only if you include the 0 and infinity end points, otherwise it is - 1/12

>>10568964
>proving addition with multiplication

Circular dependency detected

>>10568949
There is nothing to prove

>>10570696
how doesnt it