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January 20th, 2016, 09:23 PM   #1
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zylo Definition of Empty Set

Definition: An empty set is an emptied set.
An empty set has its origin in some set, specified or unspecified.
In zylo's axiom system* an empty set is not a set.

Conventions
All empty sets are considered the same thing. There is no distinction made between an empty set of elephants or an empty set of numbers (no 01,02,... just 0)
The empty set is a member of every set.
The empty set may be given other properties or definitions as desired or required.

Alternate definition: An empty set is a set without members (no emptied source set, implied or specified). In zylo's axiom system* there is no such thing.

*
Set: Things for which = and ϵ are defined.
Axiom 1: A = B and A ϵ B are mutually exclusive.
Axiom 2: A is a set iff B exists st B ϵ A.

Last edited by zylo; January 20th, 2016 at 09:31 PM. Reason: add zylo axiom system
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January 20th, 2016, 10:11 PM   #2
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In zylo's axiom system, give an example of a set with the minimum possible number of elements. How many elements does it have?
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January 20th, 2016, 10:37 PM   #3
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Quote:
Originally Posted by skipjack View Post
In zylo's axiom system, give an example of a set with the minimum possible number of elements. How many elements does it have?
A={B), B $\displaystyle \epsilon$ A
A has one member (element).

The convention that 0 is a member of every set is not part of zylo's axiom system.

My wife wants me to get a generator started for an impending storm- I may be a while.

Last edited by zylo; January 20th, 2016 at 10:44 PM. Reason: add "the convention that..."
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January 21st, 2016, 12:03 AM   #4
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Quote:
zylo's axiom system.
You appear to be ignoring my ojection that your first 'axiom' leads to a contradiction or paradox.
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