Develop a strong foundation and understanding of web design by learning HTML, CSS, and additional tools to help you develop your own website.

What's the way to prove that 1 = 1

Experts Exchange Solution brought to you by

Enjoy your complimentary solution view.

Get every solution instantly with Premium.
Start your 7-day free trial.

I wear a lot of hats...

"The solutions and answers provided on Experts Exchange have been extremely helpful to me over the last few years. I wear a lot of hats - Developer, Database Administrator, Help Desk, etc., so I know a lot of things but not a lot about one thing. Experts Exchange gives me answers from people who do know a lot about one thing, in a easy to use platform." -Todd S.

in other words, axioms cannot be proven nor disproven, they are facts . Every science has axioms, even reigions have something like axioms - eg. that God exists (for christians).

Another important point is that axioms are like groundwork of a building - if they were disproven, whole structure of a science built on this axiom would fall.

There were attempts to prove that 1=2, but most of them have one big catch - dividing by zero...

For example, we could use alittle algebra and rearrange the terms so we have : 1 - 1 = 0, but that already assumes we believe in the correctness of algebratic operations, and the orrectness of arithmetic, and that anything minus an equal amount equals "zero".

One possible approach is to say: If we are going to be able to prove anything at all, we have to make a few assumptions, such as the location of a symbol on a page does not change its value, and a symbol is always numerically equivalent to itself. If we can't make those assumptions, then nothing else we write is going to manke any sense, so we might as well just ASSUME that A = A, for all A, assuming A is a constant. There's probably a logical proof of this in Principia Mathematica.

Experts Exchange Solution brought to you by

Your issues matter to us.

Facing a tech roadblock? Get the help and guidance you need from experienced professionals who care. Ask your question anytime, anywhere, with no hassle.

Start your 7-day free trial1 is a constant by Definition (Integer = Constant)

Let A equal the value of the constant '1'

therefore, A=A or 1=1

u can also elaborate an algebra that sais that

1!=1

Well, you can, but what sense has algebra that states that constant isn't equal to itself? It'll mean that anything is equal to anything!

1. try to prove the opposite of the 5th axiom, that is:

a. assume that NO parallel line can be drawn through the point that is parallel to the line, and

b. assume that at least TWO parallel lines can be drawn through the point and parallel to it.

2. disprove assumptions a & b using the first four axioms

3. using a "double negative" attack, if all other possibilities were exhausted and proven to be false, the remaining (which is the original 5th axiom) must be true.

sounds like a master plan, right? the problem was, after doing #1, they were unable to do #2, which is understandibly the hardest part. as a matter of fact, these assumptions gave rise to two very important geometries, which are spherical geometry and hyperbolic geometry. they were unable to succeed in their mission, but it produced good results just the same.the end.

now, if you're thinking on how to prove an entire axiom, i am telling you two things:

a. you may want to try to assume that 1=any number greater than 1 and/or 1=any number less than 1 WITHOUT reflexivity then disprove both assumptions. you got yourself a proof. that is, if you can find something else to use withot reflexivity.

b. good luck on your search. this may sound sarcastic, but those mathematicians faced severe criticism by the math community before being able to come up with their discovery. come to think of it, who knows? you may be able to find that proof and topple down the foundation of mathematics just like einstein did with physics!

for anything it's worth,

Centeris

>I think maimran wants the logic behind the axiom

What logic do U mean? there's no logic behind axioms...

Just a thought:

two guys had both one dollar note in their pockets. Both of them have spent whole dollar. now they have both no money in their pockets.

So, they had both certain number of one-dollar notes (one), now they have none.

Conclusion: they had equal number of one-dollar notes.

how do we know if the dollar one guy had has the same value with the very dollar the other guy had in his pocket? because a dollar is a dollar? isn't the assumption the conclusion that we want? you know what i mean.

but what he said is true. the axiom IS the logic and supposedly, it can no longer be broken down to smaller principles.

peace out!

Centeris

A thing is itself,

no matter who is talking about it, or how they are refering to it

> divide by (a^2-a*b) ...

this is is invalid operation:

if a=b, then a^2=a*b.

result of substracting of 2 equal number is zero.

we can't divide by zero, so this is the reason why you get such result

Math / Science

From novice to tech pro — start learning today.

Experts Exchange Solution brought to you by

Enjoy your complimentary solution view.

Get every solution instantly with Premium.
Start your 7-day free trial.