# Thread: Counting elements

1. ## Counting elements

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

2. Originally Posted by acc100jt
I understand that {1, 2}={1, 2, 1}.
But do they have the same number of elements??????

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

3. Originally Posted by CaptainBlack
so maybe
your question is really about something else?
Perhaps he was told to prove that,
$\{1,2\}=\{1,2\}$
Have the same number of elements?
------
If so then consider the map,
$\phi:\{1,2\}\to \{1,2\}$
defined as, $\phi(1)=1$ und $\phi(2)=2$. Then it is a bijective map. And the prove is complete.

4. 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.