Question

simple question !
but why 1+1=2!
perfect logic is needed!
perfect steps! of solving
and correct formulae

Answer 1

because 2!=2*1=2
and 1+1=2
what's the problem?

Answer 2

no logic! no formulae!

Answer 3

@Kreshnik

Answer 4

@Rohangrr \[\LARGE n!=n\cdot (n-1)\cdot (n-2)\cdot \;\;\; ...\;\;\; \cdot (n-n+1)\]
Tell me a logic about why
\[\LARGE 5!\neq 3\]
then you'll know what I mean !

Answer 5

5*4*3*2*1 = 120
1+2+0 = 3
5! = 3
Bam!

Answer 6

@m_charron2 LOL.... let's see what logic @Rohangrr will tell us, and what "perfect formula" also ! :P

Answer 7

Are you asking for a proof of addition, or a proof of the Fundamental Theorem of Arithmetic?

Answer 8

Why does 1+1=2?
If someone demanded proof that 1+1=2 is true what would you do? Would you get an object and place it next to another object and then count them? One might argue that that doesn’t prove that 1+1=2 because 1+1=2 is a necessary truth and you cannot get necessity from experience (as per the history of philosophy). If one thought that all knowledge comes from experience one might then, like Quine, think that it is possible that we could have experience that dis-confirmed mathematics. For instance David Rosenthal has argued that if we ever had irrefutable counting evidence (i.e. widespread, re-created and independently confirmed) that 1+1=2 were false then we would have to admit that it was false and so mathematic is contingent on experience. Yikes!
Or would you appeal to the Peano axioms, which include the claim that 0 is a number and that it has a successor denoted by S(0) and then define addition as
(for all a) a+0=a
(for all a and b) a+S(b)=S(a+b)
So then it is easy to show that 1+1=2 as follows
1+1=a+S(0)=S(0+1)=S(1)=2
But then one might worry about the successor relation. It might seem as though we have simply assumed addition in the definition of the successor relation (i.e. it tacitly assumes that S(a)=(a+1)).
Of course we can show that S(a)=(a+1) by the definition of addition above. So, let S(0)=1 then a+1=a+S(0) by the definition of addition we get a+S(0)=S(a+0) and since a+0=a we get S(a) so (a+1)=S(a). But then we seem to have assumed addition by stipulating that S(0)=1 (as we actually did in the initial proof of 1+1=2…worse and worse!)
Is the claim that when you have nothing and add a thing you then get only the one thing (i.e. S(0)=1) supposed to be a truth that we just apprehend with pure reason? A self-evident truth that is ‘clear and distinct’? Or something that experience has trained us to believe? Is there any non-question begging reason to prefer either of these?

Answer 9

I'm not going to read that !!

Answer 10

@Kreshnik here's u r ans...

Answer 11

get me here the whole Wiki, let's see what we can get ! O_O @Rohangrr

Answer 12

@Kreshnik dont spam

Answer 13

am I spamming ?

Answer 14

As it happens there are other Lemmas and Postulates we use, that can be a bit of a mess--some of them we know to be false.

In this case, however.
Let's Assume:
1+1 =/= 2
a+a= 2a would still be true. because THAT is a Postulate. and math would still stand--we would just use different numbers to represent the abstractions.

Answer 15

@agreene there he is

Answer 16

For an example of a known false, take Euclid's 5th Postulate:
"That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles."

If this were true, then only Euclidean space would occur, and we wouldn't have things like--you know, GPS or Modern Physics.