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bio website dcproof.com
location Canada
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An amateur mathematician, I have developed DC Proof, an educational software program to introduce students to the basic methods of proof. In the style of most mathematics textbooks at the undergraduate level, its simplified rules of logic and set theory are loosely based on standard FOL and ZFC. For more information, a video demo and free download, visit my website at http://www.dcproof.com.

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Apr
12
comment Need help with a fundamental theorem of finite arithmetic
I can't make this work either. Thanks anyway.
Apr
10
comment Need help with a fundamental theorem of finite arithmetic
I misunderstood your comment about "a good third axiom." I will try using it as third condition for constructing $f$.
Apr
10
comment Need help with a fundamental theorem of finite arithmetic
By "inductively defined subset," I meant the smallest subset satisfying those conditions. I can prove, for example, that $(0,0,S(0))\notin f$ if $0\ne m$. It may come to just assuming it with an axiom, but where's the fun in that?
Apr
10
revised Need help with a fundamental theorem of finite arithmetic
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Apr
10
revised Need help with a fundamental theorem of finite arithmetic
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Apr
10
revised Need help with a fundamental theorem of finite arithmetic
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Apr
10
asked Need help with a fundamental theorem of finite arithmetic
Apr
8
comment Examples of partial functions in which the domain is not known?
@QiaochuYuan Only the OP can say for sure if this answers her question or not, but it seemed to me that she had an incomplete understanding of what a partial function is. She did not seem to understand that, to prove that a relation is a partial function, you do not need to specify its domain.
Apr
8
comment Examples of partial functions in which the domain is not known?
@QiaochuYuan I provide an alternative definition of a partial function that makes no mention of a domain. I find it more useful than the usual definition (e.g. at Wikipedia) that explicitly mentions a domain. I also give some examples.
Apr
8
revised Existence of an axiom question in relation to $\mathsf{Infinity}$
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Apr
7
comment On ambiguity in statements expressed in natural language, where the statements use an indefinite article, e.g. “a”.
From your examples, you might consider something like: 1. Every house is a kind of building. 2. A certain house is being built next to our house.
Apr
7
answered Existence of an axiom question in relation to $\mathsf{Infinity}$
Apr
7
revised Examples of partial functions in which the domain is not known?
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Apr
7
revised Examples of partial functions in which the domain is not known?
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Apr
7
answered Examples of partial functions in which the domain is not known?
Mar
23
revised The ultrafinitary equivalent of the Peano axioms?
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Mar
19
comment How is $\{\emptyset,\{\emptyset,\emptyset\}\} = \{\{\emptyset\},\emptyset,\{\emptyset\}\}$?
Using the rules given by MJD, prove that both sets are equal to $\{\emptyset , \{\emptyset\}\}.$
Mar
19
comment Why isn't the inductive set _the_ set of natural numbers?
I'm no expert on ZF, but the axiom does not rule out the possibility of other "junk" being in $x$ in additional to elements of $N$. To obtain $N$, you must obtain the intersection of all sets like $x$.
Mar
19
comment What background is needed to start Set Theory?
For a more interactive approach, may I humbly suggest my proof-checking software with accompanying tutorial. It may be more directly applicable to your situation than a textbook devoted to set theory. Visit my website for a video demo and free download at dcproof.com Write to me if you have any problems at all.
Mar
19
accepted The ultrafinitary equivalent of the Peano axioms?