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/sci/ - Science & Math

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4913431 No.4913431 [Reply] [Original]

I propose a challenge for you, /sci/.

>> No.4913434

Not math.
Math is about making stuff simpler not harder.

>> No.4913433

>>4913431

Inb4 Bertrand Russel's clusterfuck of a proof

>> No.4913437

>>4913434
Did you make up that definition of math. Good for you. I go by the dictionary definition.

>> No.4913451
File: 11 KB, 300x393, ayn-rand-wtl_big[1].jpg [View same] [iqdb] [saucenao] [google]
4913451

It's a special case of A=A.

>> No.4913476

the definition of 2 is that it's 1 + 1. it's an axiom.

>> No.4913477

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.

>> No.4913488

>>4913477
Quite wrong:
P1. 0 is in N
P3. There is no x such that x' = 0

>> No.4913491

>>4913488

read the end mother fucker

>> No.4913511

>>4913431
1 = lim 0.9....9 (9 repeating n times)
so 1+1 = lim 1.9....98 (9 repeating n-1 times)
however that limit can be evaluated using math:
1 + 0.9...9 (n times) - 0.0...01 (n-1 times) -> 1+1-0 = 2

>> No.4913517

>>4913511
this doesn't proof 1 + 1 = 2 you newb.

>> No.4913518

>>4913517
oh gosh i didnt realize

>> No.4913631

>>4913511
1 = lim 0.9....9 (9 repeating n times)

>Nope.
If the 9's repeat n times, that means they repeat an, (albeit unspecified), FINITE number of times. hence the limit of 0.9....9 (9 repeating n times) is 0.9....9 (9 repeating n times), not one.

1= lim 0.99... (repeating infinite times) would be correct. On a side note, it still doesn't prove the original postulate.

>> No.4913682

And what is the point of this? This follows directly from the Peano axioms. Do you suggest we use some other axiomatic system just to make it harder to prove?

>> No.4913698

1+1 equals two because I will kill anybody who says otherwise.

>> No.4913706

I believe it.

>> No.4913711

>>4913706
I don't.

>> No.4913713
File: 6 KB, 240x273, stirner.gif [View same] [iqdb] [saucenao] [google]
4913713

>>4913711
you're just a spook

>> No.4913715

Do Peano axioms assume the laws of thought?
I'd like a true confluent/convergent recursive definition that does not use the 3 laws of thought (not that I don't believe 1+1=2, but I am interested)

>> No.4913714

>>4913682
Fun. some people have it.

>> No.4913722

1+1=2 because 2 is the most boring possible answer to "What is 1+1?"

Similarly, the answer to all of the questions similar to "Why life is like it is", "Why is there life on Earth", "Why do humans look like this", etc.. is: Because that's the most boring way it could have happened.

"Why must things happen the most boring way possible, then?" You may ask. The answer is simple: Because that's the most boring way the entirety of all things could possibly be structured.

>> No.4913725

>>4913714
Fun can be had on /b/ or /v/, not on /sci/.

>> No.4913727

>>4913725
One time you had fun, but it was awful? Same here, man, same here.

>> No.4913728

>>4913714

If you find it fun, then I guess go ahead. What about doing something fun and worthawhile, like set or number theory?

>> No.4913731
File: 22 KB, 251x226, laughingwhores.jpg [View same] [iqdb] [saucenao] [google]
4913731

>>4913728
>set and number theory
>worthwhile

>> No.4913743

>>4913725
>/v/
>fun
Well, I... guess you've never been there

>> No.4913756

<span class="math">OK~SO~ME~AND~MY~FRIEND~JIMMY~BOTH~HAVE~A~ROCK~EACH.~SINCE~ME~AND~JIMMY~ARE~SUCH~GOOD~FRIENDS~WE~DECI
DED~TO~COMBINE~OUR~ROCKS.~WE~BOTH~PUT~OUR~ROCKS~IN~THE~MAGIC~BOX~OF~DESTINY~AND~STARTED~SHAKING~IT~L
IKE~CRAZY.~AFTER~A~FEW~MINUTES~OF~THIS~WE~OPENED~IT~UP~AND~WE~HAD~TWO~MOTHER~FUCKING~ROCKS~NEXT~TO~E
ACH~OTHER.[/spoiler]
<div class="math">IT~WAS~A~GOOD~DAY~INDEED</div>

>> No.4913758
File: 244 KB, 718x1024, 1342216777784.jpg [View same] [iqdb] [saucenao] [google]
4913758

>>4913431
First of all, we need to simplify that mess of an equation you posted.
Pic related.

>> No.4913762

>>4913758

>engineers
>in charge of maths

bound to fail.

>> No.4913763

>>4913756
BUT WHAT IF YOU AND JIMMY WERE ON ANOTHER PLANET LIKE MARS THAT FOLLOWED DIFFERENT LAWS OF PHYSICS AND WHEN YOU OPENED THE BOX THERE WAS ACTUALLY Pi*3-5i ROCKS!!! AND WHAT IF OBSERVING THE ROCKS AFFECTS THE AMOUNT OF THE ROCKS?!? YOU CANNOT KNOW FOR CERTAIN THAT 2 ROCKS DIDN'T APPEAR JUST BECAUSE YOU WANTED THEM TO APPEAR!

>> No.4913764

>>4913756
When you put rocks in a box and shake the box, you'll get sand.

>> No.4913777

>>4913758
What book is that from?

>> No.4913797

>>4913758
Good. Good.
Now we can finally start to understand the proof in >>4913477.

>> No.4913802 [DELETED] 

>>4913797
>>4913777
>>4913762
It's a joke against engineers, yes I'm a genius for figuring this out

>> No.4913803

>>4913777
none, it's a joke against engineers

>> No.4913860

1+1 = 2
[-1]
1=1
[+1]
2=2
hence 1+1=2 :)

>> No.4913895

0 = {}
n+ = n ∪ {n}
0+ = {} ∪ {{}} = {{}} = 1
1+ = {{}} ∪ {{{}}} = {{}, {{}}} = 1+1 = 2

>> No.4913907

>>4913895
This isn't a proof.

>> No.4913963

>>4913758
This is hilarious.

>> No.4914040

>>4913963

is it really HILARIOUS?

did you actually find it FUNNY?!

HA HA HA HA HA HA HA THE MIRTH

>> No.4915044
File: 61 KB, 680x1146, PrincipiaMathematica.png [View same] [iqdb] [saucenao] [google]
4915044

"From this proposition it will follow, once arithmetical addition has been defined, that 1+1=2." - Page 392 of Volume I of the Principia Mathematica.

Addition doesn't get defined until page 82 of Volume II.

>> No.4915157

>>4913895
What kind of ungodly notation is this?

>> No.4915861

>>4915157
its just the union of sets and the cardinality of sets.
are you 12?