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Thread: Can {0} be considered as empty set?

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    Member Array Bossness's Avatar
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    Default Can {0} be considered as empty set?

    And if no, why not?

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    erhmahgahwdyewguise Rat n Roll Pinball Champion Array Jynweythek's Avatar
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    Because it's not empty.

    eDIT: I'm not a mathematician, so if somebody wants to come along and tell me I'm wrong, please do so.

    Anyway, think of it like this. The set can be thought of as a room. Inside the room, there is a box, but the box is empty. This is {0}. If there were something in the box, say one rock, it would be {1}. If there were two empty boxes, it would be {0,0}. If you climbed inside one of the boxes, it would be {0,you being silly}. Etc. Get it? It's all boxes.
    Secret forum

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    Member Array edstamos's Avatar
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    It's just a symbol. If you define {0} as an empty set, you can write it that way. However, it can be argued that {0} is a set with one element which has a real value of 0.
    Best to be explicit.
    "If you're not part of the solution, you're part of the precipitate." ~Henry J. Tillman

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    But it is

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    Quote Originally Posted by edstamos View Post
    It's just a symbol. If you define {0} as an empty set, you can write it that way. However, it can be argued that {0} is a set with one element which has a real value of 0.
    Best to be explicit.
    My point exactly, the element is zero. That's like say "I have one thing and that thing is nothing"

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    *saying

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    Member Array edstamos's Avatar
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    0 is not in the set of positive integers, or the set of letters {A,B,C,Z}. By putting 0 in the set by default, you are confining the parameters of your set.

    If you're familiar with arrays, an empty set correlates to an array with size zero, and {0} is an array with size 1 and that element having a value of 0.
    "If you're not part of the solution, you're part of the precipitate." ~Henry J. Tillman

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    Quote Originally Posted by edstamos View Post
    0 is not in the set of positive integers, or the set of letters {A,B,C,Z}. By putting 0 in the set by default, you are confining the parameters of your set.

    If you're familiar with arrays, an empty set correlates to an array with size zero, and {0} is an array with size 1 and that element having a value of 0.
    Not really. By putting {0} I'm implying the set is empty in an unconventional (and somewhat paradoxial way). If I put {0,1}, then we can talk about parameters

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    Member Array edstamos's Avatar
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    Like I said, if you write something along the lines of:
    Let {0} represent the empty set

    then it's fine. But why would you want to represent a simple idea in an unconventional and paradoxical way except to obfuscate the intent of your work?

    Don't get me wrong, someone reading your work will might know what you mean when you write {0} without a definition, but this assumption should not be made.
    "If you're not part of the solution, you're part of the precipitate." ~Henry J. Tillman

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    Quote Originally Posted by edstamos View Post
    Like I said, if you write something along the lines of:
    Let {0} represent the empty set

    then it's fine. But why would you want to represent a simple idea in an unconventional and paradoxical way except to obfuscate the intent of your work?
    Just a random thought. It all started when I thought about this;

    A = {x: x = 0}
    A = {0}
    Is A an empty set?

    That was my thought pattern before this post. I really wasn't trying to be confusing or unorthodox.

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