/lit/ - Literature

[Anonymous No.13817433]

Since you guys are so smart:

>prove to me, that 1+1=2

[Anonymous No.13817442]

>>13817433
It doesn't. I'm sorry your mother never loved you enough to read you fairytales, but 1+1 makes lots of babies and live happily ever after, the end.

[Anonymous No.13817445]

The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:

P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
(using P1 and P2). If b isn't 1, then let c' = b, with c in N
(using P4), and define a + b = (a + c)'.

Then you have to define 2:
Def: 2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem: 1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
If b isn't 0, then let c' = b, with c in N, and define
a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:

Proof: Use the second part of the definition of + first:
1 + 1 = (1 + 0)'
Now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D.

[Anonymous No.13817564]

>>13817445
Boring

[Anonymous No.13817644]

>>13817433
If a=1, b=2 and a+a=b
Then 1+1=2
Q(uite)E(asily)D(one)

[Anonymous No.13819316]

>>13817644
who said a+a=b?
not a proof

[Anonymous No.13819322]

[Anonymous No.13819333]

>>13817433
tree + tree exquals treetree

[Anonymous No.13819373]

>>13817445
Almost perfect anon but you forgot to model the Peano axioms using ZFC set theory as your foundations.

[Anonymous No.13819377]

>>13817445
Based

[Anonymous No.13819440]

>>13817433
As a math major who studies philosophy as a hobby, I can say something confidently at this.
Questioning what the proof why is 1+1=2 is no different from the philosophical question of what is mathematics - what is the essence of mathematics.
And now this philosophical problem is like another "that one". It's like asking what the definition of art is.
>The definition of art is controversial in contemporary philosophy. Whether art can be defined has also been a matter of controversy. The philosophical usefulness of a definition of art has also been debated. (Stanford Encyclopedia)
So people say another things. giving opinion at different questions. answer of non- relevant but at least certain and clear questions. The professor's advice of "please don't study the foundations of mathematics."
Because I can't finish it like this-like other people, so I want to change the question to how the mathematician thinks.

Then, what Godel said become most relevant.
>7.0.2 mathematics describes a non-sensual reality, which exists independently both of the acts and the dispositions of the human mind and is only perceived, and probably perceived very incompletely, by the human mind.
>7.0.3 Mathematical objects and facts (or at least something in them) exist objectively and independently of our mental acts and decisions.
The important thing is that mathematicians keep a stand this Godel's position on philosophy of mathematics as time goes on - Platonism that too much to be Platonism.

[Anonymous No.13819482]

>>13819322
that is actually not a real proof of 1+1=2. the 1 and 2 in this proof is actually an "ordinal" number. 1 and 2 we always use is the cardinal number. Cantor argued that this should be separated, and Whitehead and Russell gave a strong support on this so ordinal is first.
The real proof of 1+1=2 in Principia Mathematica is happened in 300 pages later. with the necessitation of axiom of infinity.

[Anonymous No.13819487]

>>13817433
Math is only a theory so you can't. It's why I'm agnostic. Knowing things is not possible ergo nothing can be proven. You can program a computer to output incorrect math using binary, but the number one doesn't exist. You can divide it indefinitely, according to mathematical theory; but does infinity really exist? If not, how many numbers are in the number one? How many points does a circle have? Math is less literal than you think. Literally why did we make it? To unevenly count the days, to pretend that all apples are the same size when they're not? It was never necessarily about truth but more so the art of accurate guesswork.

[Anonymous No.13819601]

>>13817433
Math originates from the perception of objects, which is why mathematicians are always going on about countable things and shy the fuck away from the uncountable. One and two and plus can therefore only be understood in terms of accounting or the accumulation of things, and namely, "two" is how many things you have if you have one thing and then get one more thing. And of course, plus is what we call it if you have two piles of things, and you combine them.
And to close with the obvious next question, minus is when you take things away, but if you want to understand negative numbers, you have to first understand debt.

[Anonymous No.13819610]

>>13817433
It doesn't. Go to the lumber yard. that 2x4 is probably a 1 3/5x 3 1/3.

[Anonymous No.13819629]

>>13819601
bro what about imaginary number and vector

[Anonymous No.13819641]

| + | = ||

[Anonymous No.13819763]

Actually math isn't based on logic and such nonsense, it's a useful cultural convention that we use to model reality. Fuck, logicism is wack bro.

[Anonymous No.13819812]

>>13819763
That doesn't explain Euclid's obsession of proof

[Anonymous No.13820121]

1+1=2 simply because we define "2" as being composed of two "1"s. It is no more truth than any other thing which is defined by humans.

[Anonymous No.13820140]

>>13817445
Okay, I reject all of your premises. Prove them.