does anyone know of a mathematical (or physics based) proof for 1=1?

Question

I've heard vague rumours that there is a proof that 1=1, but I cannot seem to locate this proof anywhere - I may be mistaken, but if not, does anyone know what this proof is, or where I would be able to find it? The context was a physics post-gradute who allegedly prooved this to someone I know (who wasn't the least bit interested!)

Answer 1

Mathematicians Whitehead and Russell spent years establishing the logical foundations of mathematics, leading up to the proof that 1 = 1. Check out their work, "Principia Mathematica" (link below). Unfortunately, not only the proof itself (including prepratory work) is long and difficult, other mathematicians such as Godel have challenged the completeness of the proof. In other words, the equation 1 = 1 may have to be taken axiomatically. Most people find it silly that mathematicians would need to try to prove that 1 = 1, but it's a serious matter in axiomatic set theory.

Answer 2

The only proof I know of is the identity proof, which I don't think is what you're asking for. Sorry.

However, being the nerd that I am, I have to point out the error in Blue Sky's "proof." He divided by zero. Since A=B we know that (A-B)=0. As any algebra 1 teacher will beat into our head - YOU CANNOT DIVIDE BY ZERO! You'll get all sorts of goofy errors, like 1=2.

Answer 3

the question is actually more metaphysics than physics. for the proof of 2 = 1 you cant divide anything by 0 and thats what is being done one of the steps, also there is a place wher u are multiplying B by 0 which is stil 0

Answer 4

You don't need any mathematical proof to know that you are you 1 is always 1 and 2 is always 2. this is a statement of facts. Don't crack your brain into thinking too much. anything you see is equal to that thing not anything else.
Assuming somebody told you that you are equal to something else then it is there that you will ask for a prove.
if you are told a=b then if a=1 b must also be =1 that is the logic

Answer 5

Here's your proof:

- hold an apple in one hand
- count how many apples are in your hand (should be 1)
- look away
- look at your hand again and count the apples (should be 1)

as long as no apples were added or deleted from your hand, then the results of the first observation are equal to the results of your second observation...hence 1 = 1

See, wasn't that simple to understand?

Yes, I'm being sarcastic...but come on...is life really so complicated that someone needs to prove that 1=1? Heck, my kids know that one!

Answer 6

I don't know about that one, but I do have a proof for 1=2
Yes we have proven that 1=2, it's amazing what can happen when you put an engineer and a six sigma in a bar together with lots of alcohol.

Answer 7

Try using mathematic induction to prove that 1=1. Refer to :
http://zimmer.csufresno.edu/~larryc/proofs/proofs.mathinduction.html

Answer 8

Its proven by identity, however it can be proven that 1 = -1

the sqare 1 =1, the square of -1= 1, as such the square route of 1 = -1 or 1 meaning that 1=-1!

Answer 9

A form of that (A=A) is referred to as the 'law of identity'. And there are whole books written about it. One of the first was probably Aristotle, who mentions in rather famously in the 'Metaphysics' work (book 7, part 17, to be precise).

Hope that helps!

Answer 10

scythian is on the mark right here: the useful integers are carefully built utilising Peano's axioms, and a million+a million is the instant successor of a million, that's defined as 2. yet i could fully disagree with scythian's argument that Godel's Incompleteness Theorems are arguable; the only mathematicians that heavily sense this way are fringe logicians and maniacal set theorists. Godel's theorems unfold out alot of recent venues in arithmetic, and a few would say "freed" us from the purely approximately specific rigorous loss of life to which we've been headed. certainly, Hilbert in 1900 asked "ought to somebody please set up a equipment of axioms that's thoroughly consistent and serves as a foundation for all math?", to which Godel replied, numerous years later, "no, no you could; any axiomatic equipment describing the integers could have specific unprovable statements, and a few that are consistent whilst taken care of the two as authentic and as fake." To summarize: a million+a million is two by using fact it particularly is defined that way, axiomatically, and subsequently won't be able to be shown decrease than the conventional equipment of Peano's axioms. Steve EDIT - Above, once I say "unprovable statements", I mean statements taken care of as authentic, yet no longer proved as such (no longer inclusive of axioms). once I communicate a pair of assertion being "consistent whilst taken care of the two as authentic and as fake", I mean self reliant of the present axiomatic framework; it particularly is resembling saying the framework won't be able to instruct its very own consistency.