The result, you eventually arrive at something that has to have existed infinitely, regardless of what you call it and regardless of what attributes you give it. — GigoloJoe
Ultimately, you arrive at either a) nothing, or b) something. — GigoloJoe
You just keep on moving to the left one step at a time forever. — fishfry
Umm... geometry doesn't need calculus. You can draw geometry, you can draw a circle, you know. With geometry you already get the mathematical constant called Pi. No computation needed.Pi is a number, but doesn't come into existence until calculated. It is the product of an equation. Absent the equation or at least prior to the existence of the equation it is just set of numbers without meaning. — GigoloJoe
Umm... geometry doesn't need calculus. You can draw geometry, you can draw a circle, you know. With geometry you already get the mathematical constant called Pi. No computation needed. — ssu
And if with the exception of Chaitin's constant all mathematical constants are computable numbers, don't fixate on just the computability. — ssu
Is making a drawing computation?You did do a computation. You gave a finite-length description of a particular real number. The numbers for which you can do that are the computable reals. — fishfry
Of course, but I was talking about Mathematical constants. Now there are a lot of transcendental numbers that we simply cannot define.You see a number that is transcendental and "close to" Pi isn't an accurate definition that pinpoints to one exact number.If all you have is the computable numbers, your real line is full of holes. The computable real line is NOT a model of Euclidean geometry. For example two lines in the plane made up only of points whose coordinates are computable, may pass through each other without intersecting. — fishfry
Exactly, but us not being able to define them (to compute them) doesn't make them not to exist.Of course pi is the output of a computation, as is the number 3. Most real numbers, and most points on Euclid's line, are not the output of any computation or finite-length description. — fishfry
How is it an approximation?Pi is a mathematical approximation — Rank Amateur
Either a) nothing or b) something. — GigoloJoe
This is absolutely crazy. Irrational numbers and transcendental numbers ARE NUMBERS.because it is not an exact numerical relationship of the physical relationship — Rank Amateur
Please read again your number theory.by definition, an infinite,non-repeating decimal is an irrational number. An irrational number is not an exact anything. — Rank Amateur
Mathematics is a theoretical science. It's logic doesn't follow the limitations of making physical measurements. — ssu
Is making a drawing computation? — ssu
I think there is somewhat of a hang-up on when the numbers come into existence. Pi is not the best example to try to bring up though as even if we contend that Pi is infinite, it is only infinite in one direction. The beginning of Pi is clear and defined, meaning 3. There are no numbers to the left of Pi. For the lack of a better or more established term at the moment it can be thought of to have 'forward infinity' meaning extending into the future. — GigoloJoe
Well, the ratio of a circle's circumference to its diameter doesn't change how big or small a circle is. And I can point out what these two lengths are with a drawing. Now where this is on the number line is another question, but the ratio does stay the same.You can't define pi with a drawing. — fishfry
And Logical deduction is theoretical in math.You can only define pi using a train of logical deduction in a mathematical framework. — fishfry
Well, the ratio of a circle's circumference to its diameter doesn't change how big or small a circle is. And I can point out what these two lengths are with a drawing. Now where this is on the number line is another question, but the ratio does stay the same. — ssu
There is a profound difference between a physical drawing, and an abstract, idealized geometric shape. You can't draw a mathematical circle with a pencil and paper. Nor could you ever make a physical measurement of any irrational number. Do you understand that? I'm asking just to make sure we're not talking past each other on this essential poin — fishfry
I guess maybe I would argue that there is no zero dimensional co-ordinate in the pencil end — wax
and if one argues that a planet might describe a circle like this, in its orbit, one would run up against the same problem.... — wax
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