![]() ![]() Set U is finite for any n but it is unbounded in that it can be as big as you like depending on n. U= the set of counting numbers less than n Something that is finite but unbounded is on its way to being infinite but it isn't actually there yet.Ĭonsider the difference between the following two sets: We really don't have an infinite loop, what we have is a finite but unbounded loop.įinite but unbounded is an interesting concept that deserves to be better known. Question: How long does an infinite loop last? OK, mathematicians meet it all the time but perhaps not in the reality of an infinite loop. Programmers meet infinity sooner and more often than the average person. The theory of transfinite numbers was constructed by German mathematician, Georg Cantor (1845-1918) Unbounded v Infinite Even if you are not going to specialise in computer science and complexity theory, it is part of your intellectual growth to understand one of the deepest and most profound theories of the late 19th and early 20th centuries. The set of different orders of infinity or the "transfinite" numbers are an important idea that plays a role in computer science and the way we think about algorithms in general. Surely there is just infinity and that's that? You can guess that, as this is aleph-zero and not just Aleph, there are others in the series and aleph-1, aleph-2 and so on are all different orders of infinity, and yes there are, probably an aleph-0 of them. ![]() The usual infinity, or the smallest infinity if you can cope with this terminology, is usually called a leph-0, (aleph-zero or a leph-null) and is written ![]() Get to the bottom of the theory and dispel misconceptions surrounding a leph-zero and all that, with a programmer's view of the transfinite numbers. You may have heard a rumor that infinity comes in a number of different types. ![]()
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