Recent content by AdamFiddler

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    How do you construct proofs for set unions?

    The "union axiom" can be derived from the sum axiom and the pairing axiom, as well the proper definitions attached to both of these.
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    Graduate Can ZFC prevent Russell's paradox?

    The axiom of extensionality has not been replaced by the "axiom of subsets" as you call it. In fact, it is extensionality that allows the fact that any set created as a subset subject to given properties is unique.
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    Graduate Russell's Paradox and the Axiom Schema of Separation

    I guess the point is that y e y ==> (not) y e y is not a proper contradiction and so it does no damage to our set theory?
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    Graduate Russell's Paradox and the Axiom Schema of Separation

    As everybody I have read or heard on the matter claims, the Axiom Schema of Separation was concocted to resolve a paradox that results from the Axiom of Unrestricted Comprehension. The Axiom Schema of Unrestricted Comprehension as I understand it is stated as follows (forgive my lack of...
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    Graduate A Layman's Question About the Nature of Space

    Marcus, using the idea of a singularity and it's infinite density doesn't necessarily show that GR is wrong though, does it? It shows that it's predictions are only compatible with a continuous space. In other words, singularities would be possible if space were not discrete, right? Thanks...
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    Graduate A Layman's Question About the Nature of Space

    While reading Lee Smolin's book "Three Roads to Quantum Gravity" in which he talks about the Bekenstein bound and a smallest fundamental unit of area, the following occurred to me: Suppose there does exist such a smallest unit, call it A. Then there exists a smallest volume, V(a). A...