Comments by "kazedcat" (@kazedcat) on "How to Add" video.

  1. The assumption is that a set exist. If a set exist then you can use the subset rule to create a set with nothing in it.
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  2. What I mean is we can use this formula (a,b) = {{{a},{0,2}},{{b},{1,2}}} as definition of ordered pair. This formula always create a distinct set no matter what is in a and b.
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  3. If you don't define how heavy exactly is 1 pound you will have riot in the market.You don't like that 1 pound is too light well to bad you cannot change how heavy 1 pound is.
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  4. It is already define with extensionality. Two set are the same set if they have the same members.
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  5.  @khiemgom  He did not use any other property except the property of extensionality. The = sign is just a symbol to represent extensionality. It is not the same as the common equality it is more specific that represents the thing on the right and the thing on the left they are identical set. There is actually other way to represent it using only symbols of first order logic without using equality but the resulting expression is very convoluted and hard to parse compared to using = to represent extensionality.
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  6. There are sets that is not a member of the set of all natural numbers. What is interesting is that we can actually use this set {0,2} and {1,2} as tags for the ordered pair structures. Since they are not natural numbers this solves the problem of finding tags that are distinct to the sets being paired. With proper construction it can be made rigorous that no matter what elements in the set the tags will always be distinct.
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