Proove: 1 does not = 0.

Okay then, I believe that {} can be represented as zero.

By the way, my wallets content {1} day before the salary day is {}.

Originally posted by CZeke

castlerook: Yeah, that's the concept of ordered fields (fields don't in general have order), which is quite interesting. I recently attended a talk about totally ordered fields and there are some surprising things we can say about them. There are basically only a few fields they can be: for instance, if a totally ordered field is complete (all Cauchy sequence ...[text shortened]... 0

So if 1 is 0, then so is everything else in the ring, and it can only be the zero ring.[/b]

Ah! That makes sense, thank you.

I feel soooo -> 😛

Originally posted by Ramned
I feel soooo -> 😛

Don't worry, you'll figure it out some day 😉

We can even set up our own math college in this thread :p

Originally posted by Ramned
I feel soooo -> 😛

so do i. i was okay until i read this thread. and today has been quite a hardcore day so far (and its not even 11am!)-i've classified all groups up to order 15, started a program to calculate the ramsey number of (n,m), R(n,m), and i'm about to have a tutorial with a scary lecturer on, i believe, the Riemann integral.

i don't think i've ever looked at the natural numbers-they were always taken as said. it's the real numbers that are hard to define. dedekind cuts are baaaad!

Take a case of your favorite Beer (Samuel Adams for me). Drink zero of them. Not very satisfying. Now drink 1 of them...ahhh much better. Now walk away from the silly math problem and drink the rest of the beer...everything becomes much clearer.

These are questions to TheMaster37 or whoever can answer the questions I have.

I wasn't aware of the axioms of Zermelo and Frankel. But i know the axioms of Peano.

Didn't Peano cover it all? What does not Peano that Zermelo have and Frankel do have?

I short - what is the pros and cons to the axioms compared to eachother?

Originally posted by FabianFnas
These are questions to TheMaster37 or whoever can answer the questions I have.

I wasn't aware of the axioms of Zermelo and Frankel. But i know the axioms of Peano.

Didn't Peano cover it all? What does not Peano that Zermelo have and Frankel do have?

I short - what is the pros and cons to the axioms compared to eachother?

Aren't they just describing different things? Peano's axioms describe the natural numbers. The Zermelo-Frankel axioms describe set theory.

See, e.g., http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html

Originally posted by FabianFnas
These are questions to TheMaster37 or whoever can answer the questions I have.

I wasn't aware of the axioms of Zermelo and Frankel. But i know the axioms of Peano.

Didn't Peano cover it all? What does not Peano that Zermelo have and Frankel do have?

I short - what is the pros and cons to the axioms compared to eachother?

Peano describes only the natural numbers (without 0). Zermelo and Fraekel made axioms for set theory, wich includes an approach to numbers (ordinals). Z & F do have a 0 🙂

Z&F go on to describe structures of sets and prove all kinds of relations between sets and ordinals. Quite interesting if you're into math 🙂

cant you prove with logic??or is only math count as proof on these type of things

Originally posted by Ramned
wow. I bet that I can name 10 - 15 things that you guys just wrote that I do not understand, as a sophomore in H.S.

You guys, if indeed you are correct, must have taken a hardcore college class.

i'm a sophomore too!
we can be clueless together...
i always thought one factorial was one
so they lost me with that one....

as a H.S. sophomore, here's the best I can do...
using the Reflexive
Property of equality, we get:
x=x
let x=1
therefore, by the transitive property,
1=1
let us now force a zero on the right side of this equation
1=0
we get this zero by subtracting one whole number from the right hand side of the equation
simple algebra laws state that, with an equation, anything we do to one side, must be duplicaed on the opposite side in order to maintain equality...
this gives us that we must subtract one from he left side to get the balanced equation: 1-1 =0 or zero equals zero
if we do not subtract one from the left side, we get 1=0 or x=x-1

x=x-1 is not a balanced equation, therefore 1=0 is impossible