Equipollent Sets?

[BigNate]

Is {a, b, c, 0, 4} equipollent to {4, b, c, a}?

Really this is a question of whether or not we need to include the zero when considering these two. My answer is the zero does matter and so these two sets are not equipollent. Can someone with a bit more knowledge on this topic confirm this if true?

 

[ksdhart2]

More specifically, the definition used within set theory is "Two sets \(\displaystyle A\) and \(\displaystyle B\) are said to be equipollent if and only if there is a one-to-one correspondence (i.e., a bijection) from \(\displaystyle A\) onto \(\displaystyle B\)" (from Wolfram MathWorld). So, can you form a bijection between those two sets? Why or why not? How does that relate to your question of if the zero matters?

 

[HallsofIvy]

If your question is "should we include 0 in the first set?", of course we should. You are told that "0" is an element of the set.

 

[BigNate]

Thank you all for your help!