# Counting elements

• Oct 20th 2006, 03:11 AM
acc100jt
Counting elements
I understand that {1, 2}={1, 2, 1}.
But do they have the same number of elements??????

• Oct 20th 2006, 03:57 AM
CaptainBlack
Quote:

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

RonL
• Oct 20th 2006, 04:05 AM
ThePerfectHacker
Quote:

Originally Posted by CaptainBlack
so maybe

Perhaps he was told to prove that,
$\displaystyle \{1,2\}=\{1,2\}$
Have the same number of elements?
------
If so then consider the map,
$\displaystyle \phi:\{1,2\}\to \{1,2\}$
defined as, $\displaystyle \phi(1)=1$ und $\displaystyle \phi(2)=2$. Then it is a bijective map. And the prove is complete.
• Oct 20th 2006, 04:15 AM
OReilly
Quote:

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