anonymous
  • anonymous
What does it mean if a set is "closed with respect to addition?" What about multiplication?
Mathematics
schrodinger
  • schrodinger
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Mertsj
  • Mertsj
It means that whenever you add any two members of the set your answer is also a member os the set.
Mertsj
  • Mertsj
of the set. I meant
anonymous
  • anonymous
Example please?

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anonymous
  • anonymous
I'll give you sets and will you tell me if they are? {1,2}-I think no because there is no 3 {1,2,3}- think yes because 1+2=3 {1,2,3,4}-would it be because 1+2 = 3, or would it not be because 1+4 = 5
anonymous
  • anonymous
If it's the same way for multiplication, does that mean any set with a one and something else in it is closed to multiplication?
TuringTest
  • TuringTest
the set of all positive numbers is closed under addition: whenever you add positive numbers you get another positive number as an answer {1,2} is not closed under addition because 1+2=3 and 3 is not a member of the set {1,2}. it is closed under multiplication though, because 1*2=2 which is an element of the set
TuringTest
  • TuringTest
(the set of positive real numbers is also closed under multiplication too)
anonymous
  • anonymous
so it just has to have at least one number in it that is the sum or product of two other numbers in it?
TuringTest
  • TuringTest
no, {1,2,3} is closed under neither addition nor multiplication, because 3+1=4 (not a member) and 2*3=6 (not a member) so as long as there is any way to produce a member outside the set, that set is not closed under that operation.
TuringTest
  • TuringTest
...no matter that 1+2=3, there exists a way to create an element outside the set, so it is not closed
anonymous
  • anonymous
are you sure? it seems like I heard differently. But I'm unsure so I'll go with you.
TuringTest
  • TuringTest
My understanding is as I said it, and quoting mertsj: "It means that whenever you add any two members of the set your answer is also a member os the set." seems like that's the same thing here's something from online: http://mathforum.org/library/drmath/view/52452.html

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