   Must there always be a "first" thing
  I was arguing with someone over semantics, and it was an interesting debate. I was arguing that if you have a group of things that starts with 0 members at some time then, at some later time, it has members then at some point there must be a first member.Can anyone prove or disprove this? It seems like there should be some mathematical way to prove it, but I cannot think of one.   
  I don't know either way, but you would have to prove that 2 or more things couldn't occur at the same time to prove your point.   ;  What if you atomically swap members of an empty set with a set of two members?   ;  If I start with a calculator, then there is one member of the group "functional electronic items." If I take a sledge hammer to that calculator, I no longer have any members of the group "functional electronic items". What I do have is at least two members and possibly more of the group "useless pieces of garbage". But there was never just one item in the "useless" set, it was the act of converting it to the new set that made it two or more items.   ;Quote:Original post by nobodynewsI don't know either way, but you would have to prove that 2 or more things couldn't occur at the same time to prove your point.I think this was most applicable to my argument.   ;Quote:Original post by capn_midnightIf I start with a calculator, then there is one member of the group "functional electronic items." If I take a sledge hammer to that calculator, I no longer have any members of the group "functional electronic items". What I do have is at least two members and possibly more of the group "useless pieces of garbage". But there was never just one item in the "useless" set, it was the act of converting it to the new set that made it two or more items.But one of them fell first, thus that little piece of garbage was the first in the set.PROOF!   ;Quote:Original post by way2lazy2careQuote:Original post by nobodynewsI don't know either way, but you would have to prove that 2 or more things couldn't occur at the same time to prove your point.I think this was most applicable to my argument.Then your answer is: no one knows.Exciting!   ;  It's simple mathematical induction. 1. Any group that now has 1 member, at some time had 1 member. (This is trivial -- the "some time" is now.)2. For any positive number n, assuming that any group with n members at some time had 1 member, then any group with n+1 members at some time had 1 member. (This is because -- assuming that two members cannot join simultaneously -- any group with n+1 members was, prior to the most recent addition of a member, a group with n members, and thus by the assumption there was a time at which it had 1 member.)By those two statements, you show that for a group with any positive number of members, at some time it had 1 member.If you allow members to both join and leave, the argument only becomes a little more complicated.1. Any group whose maximum membership at any time in the past or present (the "group-max") is 1 member, at some time had 1 member. (This is trivial -- the "some time" is now.)2. For any positive number n, assuming that any group with group-max of n at some time had 1 member, then any group with group-max of n+1 at some time had 1 member. (This is because -- assuming that two members cannot join simultaneously -- any group with group-max n+1 was, prior to the most recent increase of the group-max, a group with group-max n, and thus by the assumption there was a time at which it had 1 member.);Quote:Original post by LockePickQuote:Original post by way2lazy2careQuote:Original post by nobodynewsI don't know either way, but you would have to prove that 2 or more things couldn't occur at the same time to prove your point.I think this was most applicable to my argument.Then your answer is: no one knows.Exciting!Winnah!   ;  Is the group multi-threaded? ;P   