/sci/ - Science & Math » Thread #13416288

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Anonymous Tue 20 Jul 18:31:19 2021 No.13416288 View Reply Original Report

Quoted By: >>13416312 >>13416381 >>13416721 >>13416727 >>13416742 >>13417029

If pi can be expressed af the ratio of a circumference to its diameter, why is it irrational? By definition, it is a fucking ratio

Anonymous

Anonymous Tue 20 Jul 2021 18:33:52 No.13416303 Report

Quoted By:

because 22/7 isn't rational

Anonymous

Anonymous Tue 20 Jul 2021 18:36:18 No.13416312 Report

Quoted By: >>13416344

>>13416288
All numbers are a ratio between two infinitely long numbers. :^)

Anonymous

Anonymous Tue 20 Jul 2021 18:45:45 No.13416344 Report

Quoted By: >>13416721 >>13416746

>>13416312
So, irrational numbers don't exist?

Anonymous

Anonymous Tue 20 Jul 2021 19:00:46 No.13416381 Report

Quoted By:

>>13416288
Similar to the way complex numbers $\mathbb{C}$ can be considered as a structure of two reals $\mathbb{R}^2$ with an appropriately defined multiplication $(a_1,b_1)\times(a_2,b_2) = (a_1a_2 - b_1b_2, a_1b_2 + a_2b_1)$ , rational numbers can be considered as a mapping of two integers $\mathbb{Z}^2$ with an appropriate equivalence relation $(p_1, q_1) \sim (p_2, q_2) \Leftrightarrow p_1q_2 = p_2q_1$ .

The "rational" in "rational numbers" only deals with ratios between integers and there is no way to make both the diameter and the circumference be integers at the same time.

Anonymous

Anonymous Tue 20 Jul 2021 20:18:41 No.13416721 Report

Quoted By:

>>13416288
>If pi can be expressed
>expressed

>By definition, it is a fucking ratio
No it's irrational, which is why it's left as an expression. Only when trying to apply it to math do you ignore the expression. Make of that what you will.

>>13416344
Neither do rational numbers.

Anonymous

Anonymous Tue 20 Jul 2021 20:20:38 No.13416727 Report

Quoted By:

>>13416288
All rational numbers can be expressed by a ratio.
But not all numbers expressed by a ratio are rational numbers.

Anonymous

Anonymous Tue 20 Jul 2021 20:24:31 No.13416742 Report

Quoted By:

>>13416288
A number is rational if and only if it can be expressed as a ratio of *integers*

Anonymous

Anonymous Tue 20 Jul 2021 20:25:13 No.13416746 Report

Quoted By:

>>13416344
They don't in the real world. All "circles" are closer to megagons.

Anonymous

Anonymous Tue 20 Jul 2021 21:50:16 No.13417029 Report

Quoted By:

>>13416288
Because you didn't read the definition of rational number carefully.

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