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John asked:
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This isn't really a question, but more of a 'Tell me your opinion' thing. Now Let me say what I've got to
say.
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Infinity is most commonly classified as having no beginning or end. Infinity seems to be such an
impossible thing to comprehend. Try to visualize it. I would say you couldn't.
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Now, take a circle. A circle can be the size of an atom, or the size of the universe. But, look at it
closer. A circle has no beginning, or an end. Just the circle.
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And, as I said, that circle could be the size of an atom, or the size of all creation, yet it has no end.
So, what I'm really trying to say is: Infinity isn't a size, or a measure, or anything of that sort. Infinity is
a property.
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What are your opinions on this?
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============
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This isn't a matter of opinion. In the above, you are not being clear on what you mean by the term
"infinity". There are several coherent meanings of this term, and very many incoherent ones. As far as
a circle having an "end"... you are confusing two senses of the word "end". One is that of the end of a
series of numbers, the other is the end of a physical object... or, alternatively, the end of a path one is
traversing. Why are you supposing those are identical? They certainly don't have to be.
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The coherent meanings of infinity are mathematical/ logical. First, you might look at any basic book
on calculus, at the section on integration. You will find that the integral, in a sense the inverse of the
differential, may be expressed as the sum of an infinite series. That is one mathematical notion of
infinity, coherent enough that most of physics and engineering uses it to build bridges, stereos, etc.,
etc. Infinity in this sense isa measure. The differential is also the limit of a series, and as such also a
measure. Second, there is Dedekind's (and others') definition of continuity, which uses a similar
notion of infinity. Again, this is quite explicitly a measure. Third, there is Cantor's notion of orders of
infinity, having to do with the size of various infinite sets. These various orders of infinity measurethe
size of sets of numbers.
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Steven Ravett Brown
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