C
cor
Guest
The cardinality of aleph-null is equal to the cardinality of the set I specified. That doesn’t mean that the set {0, 1, 2, 3…,…, aleph-null} will have all the same properties as the set {…,-2,-1, 0}. The former set has both a first member and a last member; the latter has a last member but not a first member. And you mentioned as a problem that the last member doesn’t have an immediate predecessor. But the latter set has a last member which does have an immediate predecessor, avoiding the problem you raised while still retaining an aleph-null cardinality.no, i’m not - i’m asuming that the set of elapsed moments is equal to aleph-null (aleph-null itself isn’t the “infinitieth” member of that set - i was simply being (apparently too) colloquial). if you are trying to get from one end of the set to another by successive addition, then you must work through each member of the set, which entails having to work through the gap between aleph-null and its successive constitutent numbers. which cannot be done.
aleph-null is not a member of the set I specified.this is false, i’m afraid: http://mathworld.wolfram.com/images/equations/ContinuumHypothesis/inline1.gifis at an infinite remove from 0; if it wasn’t, then the set would not be infinite, as you claim it to be. in fact, http://mathworld.wolfram.com/images/equations/ContinuumHypothesis/inline1.gifis at an infinite remove from every member of the set (which entails another problem with trying to realize an actual infinite).
I asserted that it was so with respect to the set I specified because I thought it would be obvious. The set {…-2, -1, 0} includes only natural numbers equal to or less than 0. All these numbers are in finite predecession from 0. If you disagree, name one that isn’t! One can prove it is so through transfinite induction.look, by stipulating that every member of an infinite set can be at a finite remove from 0, you are assuming what you are trying to prove: namely tht the addition of a number of finite numbers can be result in aleph-null…
I am familiar with transfinite math.look, even if you’re not familiar with transfinite math, isn’t the impossibility of something like that just obvious?
You are assuming that an infinite past has to be formed increment by increment. I think God, outside of time as we know it, can create an infinite past “all at once” as you say.i mean, remember, it’s not like we’re talking about an actual infinite being given all at once, but rather the formation of one by increment; it’s only the latter that runs into problems.