# 1 = 1 = 1

1. Aug 5, 2006

### ghostmonkey

Is every conceivable equation not simply a circular representation of 1? If F=ma, then F=F and 1=1. If a=a, then 1=a/a=1. If E=MC^2, then E=E=1=1. How is mathematics an infallible language then? We should ultimately be able to conjure up even the most complex of equations, all being equatable to 1. :surprised

2. Aug 5, 2006

What information do you get out of 1=1? You can pull out that there is an identity element, where 1 denotes a multiplicative element. Anything else? maybe... but not much.

Now take something like, $e^{i \pi} +1 = 0$.

You get a lot of information here in a small package. You get $e$ from calculus, pi from geometry, fundemental operations (+, x), and complex numbers.

So how do you build up the most complex equations from 1=1? How do you gain the knowledge to add information from nothing?

Last edited: Aug 5, 2006
3. Aug 5, 2006

### HallsofIvy

No, because in going from F= ma, to F= F you are dropping information. I could as easily say that F= ma2 and derive F= F from that, even though F= ma2 is untrue. I note you say "We should ultimately be able to conjure up even the most complex of equations, all being equatable to 1" but every example you give goes the other way. It's easy to lose information. The hard part is gaining it. If I am given 2 and 3 I can say, without question, that 2+ 3= 5. But that does not help me solve the problem "if x+ y= 5 what are x and y".

4. Aug 5, 2006

### ghostmonkey

0=1-1

Okay, I can appreciate the loss of information in going from complex to simple terms. But, regarding the x+y=5 equation, the trouble that I have is that if the sum of x and y is equal to 5, then (x+y) and 5 are identical statements, which is to say that (x+y)=(x+y) and 5=5, or 1=1.

What information is there to be gotten out of 1=1? Probably nothing, if you're looking for differentiation. Otherwise, maybe 1=1 gives us the fundamental state of the universe, which is to also say that 0=1-1. So everything in the universe is binary? Meh... :surprised

5. Aug 5, 2006

### pallidin

Well, whenever you present a x=y one can always compare it to 1=1.
But all you are doing is comparing different eqaulities, which is completely meaningless.
For example, that x=y and 1=1 could just as easily be stated as "x=y and 7.968=7.968"
Therefore, than can be no benefit in that type of comparison.

6. Aug 5, 2006

What do you mean when you say: "looking for differentiation"?

What would the fundemental state of the universe be? I don't understand... like do you mean it's age?

Last edited: Aug 5, 2006
7. Aug 5, 2006

### loseyourname

Staff Emeritus
ghostmonkey, I hate to do this to you, rather than straightforwardly answer the question myself, but you will understand the difficulty you are having much better after reading Frege's On Sense and Reference.

8. Aug 5, 2006

Interesting article loseyourname.

9. Aug 5, 2006

### Gokul43201

Staff Emeritus
Absolutely not! The first statement tells me how x and y are related; neither of the latter statements does.

Also, more specifically :
No, they are terms (or quantities, if you like); they are not statements.