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I am not a student of mathematics but dabble with its concept every now and then.

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- Thread starter Ahmed Abdullah
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- #1

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I am not a student of mathematics but dabble with its concept every now and then.

- #2

Mark44

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What do you mean by "earlier infinity?"

I am not a student of mathematics but dabble with its concept every now and then.

- #3

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What do you mean by "earlier infinity?"

Now I understand i was looking for infinity that is bigger than infinity associated with rational number but smaller than that of real number. I know that it is undecidable.

But i was originally wondering what kind of infinity is necessary for continuity in the sense of euclidean geometry.

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jbriggs444

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However, what happens when I want to know the length of the diagonal of a square of side length 1? The answer is [itex] \sqrt{2}[/itex]. What about the circumference of a circle of radius 1? The answer is [itex]2\pi[/itex].

You quickly move from rational numbers to irrational as you start looking at polygons, and then quickly to transcendental when you start looking at curves.

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jbriggs444

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Thank you for your response. I understand your point about algebraic number. If points of the plane is defined by pair of algebraic number, then the intersection of any two lines will also be a point (I get it). But i don't get your last response about computable number. I'll really appreciate if you elaborate the point.

- #8

jbriggs444

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The value of a trigonometric function or inverse trigonometric function evaluated at a computable number is, if defined at all, computable. The length of a circular arc with a computable radius between two computable endpoints is, therefore, computable.

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What are some examples of non-computable numbers?

The value of a trigonometric function or inverse trigonometric function evaluated at a computable number is, if defined at all, computable. The length of a circular arc with a computable radius between two computable endpoints is, therefore, computable.

- #10

jbriggs444

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One can nonetheless write down a definition for a non-computable number. For instance, http://en.wikipedia.org/wiki/Chaitin's_constant

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