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set theory watch

1. Is the set Y of real numbers that are less than or equal to 0 closed under addition? And closed under multiplication?
2. Closure says that if , then . This is true for addition, but not for multiplication in the set you described.
3. (Original post by Perpetuallity)
Yes. If , then . This is true for both multiplication and addition.
But...if its two numbers that are less than 0, lets say -1 and -2, multiplying them gives 2 and thats not in the set?
4. (Original post by T13)
But...if its two numbers that are less than 0, lets say -1 and -2, multiplying them gives 2 and thats not in the set?
It's not true for multiplication, I'm on autopilot here, sorry.

As you said, multiplying two negative numbers, because the set is resticted to
5. (Original post by Perpetuallity)
It's not true for multiplication, I'm on autopilot here, sorry.

As you said, multiplying two negative numbers, because the set is resticted to
Ah no problem, im just glad i understand it
The set Z of real numbers r such that −2 ≤ r ≤ 2...surely that is not closed under addition nor multiplication?
6. (Original post by T13)
Ah no problem, im just glad i understand it
The set Z of real numbers r such that −2 ≤ r ≤ 2...surely that is not closed under addition nor multiplication?
Nope, that set isn't closed for either.

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Updated: September 26, 2011
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