So I'm taking a probability class right now. We are going over elementary set theory, and the professor brought something up which seems non-intuitive to me.(adsbygoogle = window.adsbygoogle || []).push({});

He said that a set must have distinct objects, so...

[tex] A = \{ 1, \,\, 1, \,\, 2, \,\, 3 \} [/tex]

is not properly defined, because the 1 is repeated. Instead, it must be written as:

[tex] A = \{ 1, \,\, 2, \,\, 3 \} [/tex]

why is this?

I asked him then what do we do with,

[tex] A = \{ x^2 | x= -1, \,\, 0, \,\, 1 \} [/tex]

and he said that it would be,

[tex] A = \{ 1, \,\, 0 \} [/tex]

This seems weird, since in a sense we are losing information.

Would someone be so kind to elaborate on why you can't have repeated objects? I want to know why this is.

(Maybe I should have not posted this in the homework section.)

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# Probability - Set Theory Question

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