101 reputation
3
bio website pdghelicopters.com
location Scotland, United Kingdom
age 51
visits member for 2 years, 4 months
seen Apr 15 at 14:51

After scraping through an engineering degree I spent a lot of my time working for accountants.

I'm currently working for a Helicopter Charter Company where mobile web solutions are really useful.

Most of my current expertise is with Delphi 7 / MySQL / Java / Tomcat with bits of PHP and all kinds of odds and sods.


May
9
comment Are all prime numbers finite?
I suspect I'm a finitist. See foundational issues en.wikipedia.org/wiki/Finite_set
May
9
comment Are all prime numbers finite?
I think the terms finite and infinite are in fact unhelpful. I'm perfectly happy to say that the number of members has no limit and also that the "size" of the members has no limit.
May
9
awarded  Commentator
May
9
comment Are all prime numbers finite?
Or alternatively, "If one exists, give an example of a natural number that is not finite". To which I would answer "precisely". Any algorithm that generates natural numbers will by your definition always generate finite numbers. If only finite numbers can be generated, the number of them must be finite. Yes, there may always be another generated, but it will be finite. To be perfectly honest, I think this kind of stuff is undecidable.
May
9
comment Are all prime numbers finite?
"If one exists, give an example of a natural number that is not finite" How about "Start with 1. +1=2, +1=3 +1=4... repeat +1 an infinite number of times, to give an infinite numeber of members" then "There isn't a result, there are results, each and every one of which is finite. The number of results is infinite, precisely because there is no last one." I think my problem is in this. This is like having a stair case you take a step up, you take a step along, another step up, another step along.(result, member) but set theory say the staircase can be infitly long without being infinitly high.
May
8
comment Are all prime numbers finite?
Many thanks. ..
May
8
comment Are all prime numbers finite?
I'll see if I can express my problem more clearly. Start with 1. +1=2, +1=3 +1=4... repeat +1 a finite number of times and you get a finite number of results each of which are finite. Where my problem arises is that for an infinite number of members, you need to repeat this (+1) an infinite number of times and when you do that the result cannot be finite.
May
8
comment Are all prime numbers finite?
"What do we know about its elements? Well, we know that they are all finite, because all positive integers are finite." Then there must be a finite number of them. No?
May
7
comment Are all prime numbers finite?
First I'd like to thank you for taking the time to look at this. Sorry, I still don't get it. The set of natural numbers is 1,2,3,.... or 1 = member one, 2 = member two, 3=member three, etc. Each of these members is finite. I'm told that ALL natural numbers are finite. Yet there are an infinite number of members in the set. If so, how could I number the elements of set with natural numbers. I'd run out of natural numbers before I run out of members of the set which is, of course, absurd.
May
7
comment Are all prime numbers finite?
Or to put it another way, each member of the set of natural numbers, identifies itself by its number. If ALL members of the set are finite, then the set must be finite. And vice versa.
May
7
comment Are all prime numbers finite?
5024 & 5025 are both finite as is 5026, but that set only contains 5026 members, I'm not saying a maximum element must exist, I'm saying if you have an infinite number of different members of a set, then how can they all be finite?
May
6
comment Are all prime numbers finite?
"That there are infinitely many of something doesn't require that any of them be infinite, or infinity." So although there are infinitly many natural numbers, all of them are finite? So in what sense are there infinitly many? If I have 1,2,3,4 .... and all members of the set are finite, how are there infinitly many?
May
6
awarded  Supporter
May
6
comment Are all prime numbers finite?
I've always had a problem with infinity in mathematics (except in wooly as x->infinity sense). Eg, Can the members of the set of natural numbers be put into a one to one correspondence with the natural numbers? Natural numbers are not inifinite, but there are infinitly many of them... I've always had a problem with this kind of thing.
Apr
9
awarded  Autobiographer