1. B

    Axiomatic set theory ZFC is inconsistent thus mathematics ends in contradiction

    Axiomatic set theory ZFC is inconsistent, thus mathematics ends in contradiction: Axiomatic set theory ZFC was in part developed to rid mathematics of its paradoxes, such as Russell's paradox. The axiom in ZFC developed...
  2. H

    Axiomatic Systems

    Hello, this is my first post. I'm working through Euclid's Elements right now and I really love the idea of beginning with basic, intuitive axioms, and build in a systematic way to an entire structure, with a solid foundation. I've been wondering if there are other systems like this? I've been...
  3. S

    axiomatic descriptions of even size or odd size

    As I just known what is axiomatic descriptions, I still confused about how to description. Can someone help to give the axiomatic descriptions for even size or odd size to let me know it clearly. TY.
  4. Z

    zylo's Axiomatic Set Theory

    Set: Things for which = and \epsilon are defined. Axiom 1: A = B and A \epsilon B are mutually exclusive. Theorem 1: A set cannot consist of one thing. Proof: Definition of set and Axiom 1. Theorem 2: A is a set iff B exists st B \epsilon A. Proof: Definition of set, Axiom 1, and...
  5. G

    Axiomatic Theory of Economics

    Simplified Exposition of Axiomatic Economics I have written a book titled Axiomatic Theory of Economics. This book is about a new economic theory. It is not a simplified version of mainstream economics. It does not predict the future, calling neither prosperity nor ruin in America. It is...
  6. G

    Axiomatic Economics

    I have a degree in mathematics. I wrote a book about economics (Axiomatic Theory of Economics, ISBN# 1-56072-296-7) in 1999 in which I propose a new theory of economics based on three axioms: 1) One's value scale is totally (linearly) ordered: i) Transitive; p <= q and q <= r imply p <= r...
  7. L

    non axiomatic set theorem

    Hello Brothers, I'm a brazilian admirator of math and philosofy, my english is very poor, because I ask apologize antecipated. I whish yours opinion about a theorem, if I must go on, or forget about. let see: Became G a set of total possible of existence, in the form: {x e G/ x...
  8. C

    Non euclidean axiomatic

    Hi there, I've got a really peculiar question here and I didn't know who to ask to, so I'm here. I'm doing an high school work on non euclidean geometry and right now I'm analyzing Girolamo Saccheri's Euclides ab omni naevo vindicatus, here's my problem: right in his first proposition he proves...
  9. J

    What's wrong with this axiomatic proof?

    Here is a simple proof which I was told has a deficiency....can someone help point out what my mistake is? For all m,n ? Z: -m = (-1)*m Proof: m + (-1)*m = m*1 + (-1)*m by an axiom = 1*m + (-1)*m by an axiom = (1+(-1))*m by an axiom = (0)*m...
  10. L

    axiomatic definiation

    Hi all, I would like to clarify a question and my solution to it. Not quite sure if I’m on a right track. Please help me understand. If for example we assume scenario as follow "Model a system to retain information of a cyclist results competed on a several events. The results are stored in...
  11. Z

    Axiomatic theories

    Hello! I know that theorems of any mathematics theory (and more in general of any axiomatic theory) can be proved using only the axioms of such theory. Anyhow it feels kind of weird to me: I wouldn't be able to prove theorems (even the most simple ones) of the theories I know of (the last one I...