/sci/ - Science & Math

[Anonymous No.10460060]

where is proof that 1 + 1 = 2 ????

[Anonymous No.10460068]

Peano axioms. Next thread.

[Anonymous No.10460075]

>>10460068
/thread

[Anonymous No.10460181]

>>10460060
Principia Mathematica, page 367

[Anonymous No.10461824]

>>10460068
Let's count the lexicon as a letter? I know of no letterhead that forbids the number 0. We cannot use the lexicon. You must be female. There is a sociology class over there if you need us to agree. This is math. No one needs to agree with you on those grounds. Perhaps you could require yourself the use of a dictionary and say Piano next time? And they mean slide rule instead of like some name. Nice satellite funding, though.

*rolls eyes*

[Anonymous No.10461918]

>>10460060
1 + 1 = 11.

[Anonymous No.10462043]

I think I’m taking this thread way to seriously, but here I go anyway…

First, we need to clarify what we actually mean by “1” and “2.” These are numbers denoted in the decimal numeral system. Here’s a quick summary of how it works for natural numbers:
– The natural number refered to as “1” in the Peano axioms is denoted as “1”.
– To get the notation of the natural number x’ (the successor of x, in some sources S(x)), in the notation of x replace the rightmost digit by the next digit. (All digits in order: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) If the digit is a “9”, replace it by a “0” and also replace the digit to the left of the digit just replaced in the way just described (assuming a “0” where there are no more digits).

With this definition, we now know that the number denoted as “2” is actually 1’ (and obvioulsy, “1” refers to 1).

Now we just have to find out what 1 + 1 means. “+” is defined for natural numbers like this:
(1) For all natural numbers x, x + 1 = x’.
(2) For all natural numbers x and y, (x + y)’ = x + (y’).
It has to be and can be shown that this indeed defines a unique operation.

Using (1) from the definition of “+”, we get 1 + 1 = 1’. And with the knowledge from before that 1’ can be denoted as 2, we come to the conclusion that indeed 1 + 1 = 2.

[Anonymous No.10462046]

>>10460060
Because we defined two as consisting of one and then another one.

[Anonymous No.10462059]

>>10460060

[Anonymous No.10462102]

>>10462059
Ah yes, indeed. Quite so in fact.

[Anonymous No.10462149]

>>10462059
british mathematicians are such a bunch of wankers

[Anonymous No.10462159]

>>10460068
https://www.lesswrong.com/posts/zmSuDDFE4dicqd4Hg/you-only-need-faith-in-two-things

[Anonymous No.10462188]

>>10460060
How does the posi rear end work on a '72 firebird? It just does.

[Anonymous No.10462190]

>>10462159
>has never experienced motivated reasoning in his life
>has many religious friends, might convert himself

[Anonymous No.10462194]

>>10460068
>>10460075
retards and/or undergrads
>>10460060
define: 1, +, 2, =

[Anonymous No.10462368]

sounds like a linked list to these women with some kind of facts. not these but some kind.

[Anonymous No.10462426]

>>10462194

you cant just reply to a question with more questions thats not how it works buddy

[Anonymous No.10462606]

>>10460060
>proving a definition

[Anonymous No.10462908]

>>10462194
Admittedly an undergrad.

[Anonymous No.10463012]

>>10462194
Define "define: 1, +, 2, ="

[orb !aATmdo394Y No.10463047]

>>10460060
if i got one apple and i add another apple it are two apples

[Anonymous No.10463666]

>>10461918
In base 1, this is true.

[Anonymous No.10463700]

>>10463012
Define " Define " Define: 1, +, 2, =""

[Anonymous No.10464274]

>>10460060
1 is a value of one, and there are two of them
Two is two, or twice the value of a one
1+1 means that you are adding together two values of 1.
Two values of 1 becomes two
1+1=2
.


I lied, 1+1 is 11

[Anonymous No.10465121]

>>10462426
The answer to the question depends on your definitions retard

[Anonymous No.10465210]

Jokes aside can anyone dumb down the long-form of 1+1=2 proof

I don't know how to read that math notation. What's their methodology? How does that paper actually prove it?

[Anonymous No.10465215]

>>10460060
https://x80.org/collacoq/oyikofahez.coq

[Anonymous No.10465303]

>>10460068
> Peano axioms
> axioms
do you even know what this word means?

[Anonymous No.10465909]

Proof of the Limits of Sine and Cosine at Infinity
http://www.vixra.org/abs/1809.0234

[Anonymous No.10465921]

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.10465937]

>>10462606
definitions don't need to be proved here, they do need to have meaning though, otherwise further discussion seems to be futile.

[Anonymous No.10465939]

>>10463012
are you asking what the word/function "define" means?

>checkmate

[Anonymous No.10465943]

>>10462426
see >>10465937

[Anonymous No.10465947]

>>10465921
this looks cool, but i cannot understand it..
is there a ELI5?

[Anonymous No.10465982]

>>10465215
stuck here
>Cannot open . [cannot-open-path,filesystem]

[Anonymous No.10466646]

>>10463700
Define “Define “ Define “ Define: 1, +, 2, =“””

[Anonymous No.10466659]

>>10460060
1 + x = 2

x = 2 - 1

x = 1

QED

[Anonymous No.10466846]

>>10462059
That's cool, bro, but a picture of two apples would suffice. But these strange glyphs could be useful when explaining elementary facts to machines, what do I know.

[Anonymous No.10466855]

>>10465939
Define 'are you asking what the word/function "define" means?

>checkmate'

[Anonymous No.10466869]

>>10465909
Nah, on page 3, you say that if lim(x_n) diverges then lim(x_n) -> infinity in your extended real numbers. Truth is, divergence is simply a lack of convergence - that's why cyclic functions (like cos, sin) don't converge, despite having a finite range and not going to infinity.