a) { 1 }
b) counting numbers
c) integers
d) whole numbers
Can you explain please? Thanks
2007-01-22 15:50:08 · 5 answers · asked by anonymous 2 in Science & Mathematics ➔ Mathematics
"closed under division" means that, no matter which number you pick, if you divide it by any other number in the set, you get another number in the set.
1 / 1 = 1, so it works.
The others don't. For instance 1 and 2 are part of the counting numbers, the integers, and the whole numbers. But 1/2 is the result of dividing 1 by 2, and it's NOT a counting number, an integer, OR a whole number.
2007-01-22 15:56:50 · answer #1 · answered by Jim Burnell 6 · 1⤊ 0⤋
By counting numbers, I'm assuming you mean the set of natural numbers.
The set of natural numbers is not closed under division (since 3 and 4 are natural numbers, but 3/4 is not).
Neither are the set of integers and whole numbers, for precisely the same reason.
Only the set with a single element of {1} is closed under division, because the only element of the set is 1, and 1 divided 1 is 1, which still falls in the set.
2007-01-22 23:58:36 · answer #2 · answered by Puggy 7 · 1⤊ 0⤋
Pretty simple, if 0 is in any of these a,b,c, or d then it isn't closed under division. To be closed means that no matter what 2 numbers you divide by you get that same type of number
so a is definately closed. because {1} is just 1. So 1/1 = 1
b depends on what is defined as a counting number. I've seen counting numbers defined as 0,1,2,3... and also defined as 1,2,3,4.....
if it is the latter, then it is closed
c) 0 is an integer, can't divide by 0 so no
d) 0 is a whole number, can't divide by 0 so no
2007-01-22 23:56:06 · answer #3 · answered by talldude182002 1 · 1⤊ 0⤋
only a) {1}......a set is closed under division when an elements is divided by the same or another element of that set the answer should also be an element of that set...
for example, the integer 3 is an element of sets b,c and d but these sets only contains whole numbers...that is,{1,2,3,4....}
if you divide 1 by 3 the answers is 0.333333..... which is not an elemant of these sets....
2007-01-23 01:14:52 · answer #4 · answered by 13angus13 3 · 0⤊ 0⤋
The answer is a). To say that a set is closed under division is to say that when any member of that set is divided by any other member of that set the result is also a member of the set. This is true for none of the integer subsets mentioned. For instance 2 (an integer) divided by -3 (also an integer) is -2/3 (not an integer).
2007-01-23 00:01:57 · answer #5 · answered by Steve P 2 · 1⤊ 0⤋