Thread: Counting elements

I understand that {1, 2}={1, 2, 1}.
But do they have the same number of elements??????

Please help!!! Many thanks!!

Originally Posted by acc100jt

I understand that {1, 2}={1, 2, 1}.
But do they have the same number of elements??????

Please help!!! Many thanks!!

If these are sets yes they have the same elements, and so the
same number of elements. The elements of {1, 2} are 1 and 2, and
the elements of {1, 2, 1} are 1 and 2. But we would not normally
write something like {1, 2, 1} when talking about sets, so maybe
your question is really about something else?

RonL

Originally Posted by CaptainBlack

so maybe
your question is really about something else?

Perhaps he was told to prove that,

Have the same number of elements?
------
If so then consider the map,

defined as, und . Then it is a bijective map. And the prove is complete.

Originally Posted by CaptainBlack

If these are sets yes they have the same elements, and so the
same number of elements. The elements of {1, 2} are 1 and 2, and
the elements of {1, 2, 1} are 1 and 2. But we would not normally
write something like {1, 2, 1} when talking about sets, so maybe
your question is really about something else?

RonL

They have same elements, but why do they have same number of elements?

If we are talking about different elements then they have same number of elements. Talking about quantity then we have different number of elements. First set has 2 and second set has 3 elements.