General > General Technical Chat
Integers, Pi, and Number Lines.
Peter Taylor:
An integer number (or just number), should be any value that is wholly defined.
An irrational "number" is not a number, so there can be no rational "number".
These terms hark back to the days of the Pythagoreans, when they thought the Earth was the centre of the Universe.
Peter Taylor:
--- Quote from: xrunner on July 05, 2022, 02:43:31 pm ---Oh we're getting weir now, OK well ...
I give somebody an exact diameter, say it's x. I ask them to draw a circle with a circumference of pi * x. I only want an exact circle with the exact circumference.
Draw the circle on a piece of paper with a compass. Or you can use a computer with graphics if you want to. Is the circle you draw going to meet at the ends?
If you can't calculate pi exactly then how can the circle even exist before your eyes, it shouldn't have been able to be drawn in this universe - but you will do it ...
:-DD
--- End quote ---
A circle can be made to an exact (integer, or number) circumference. Cut a piece of string to that circumference, and make a circle.
A circle can be made to an exact (integer, or number) radius. Cut a piece of string to that radius, and make a circle.
What can't be done is find how long to cut a piece of string to that radius, given the length of string to make the circumference, because the ratio of the circumference of a circle to its radius is not a number, but a question.
::)
eugene:
--- Quote from: Peter Taylor on July 05, 2022, 04:41:15 pm ---An integer number (or just number), should be any value that is wholly defined.
An irrational "number" is not a number, so there can be no rational "number".
These terms hark back to the days of the Pythagoreans, when they thought the Earth was the centre of the Universe.
--- End quote ---
So now's the time to get out the toga that's been in your closet!
TimFox:
--- Quote from: eugene on July 05, 2022, 04:55:59 pm ---
--- Quote from: Peter Taylor on July 05, 2022, 04:41:15 pm ---An integer number (or just number), should be any value that is wholly defined.
An irrational "number" is not a number, so there can be no rational "number".
These terms hark back to the days of the Pythagoreans, when they thought the Earth was the centre of the Universe.
--- End quote ---
So now's the time to get out the toga that's been in your closet!
--- End quote ---
Mathematics has progressed past the time of Pythagoras, and the terms that offend the poster are now very well defined, and not in a circular method that boils down to "These concepts are icky."
The current definitions of "natural numbers", "positive integers", "integers", "rational numbers", "irrational numbers", "transcendental numbers", etc. are useful in mathematics and consistently defined.
Otherwise, one might as well ban "improper fractions" as being immoral.
eugene:
--- Quote from: eugene on July 05, 2022, 04:55:59 pm ---So now's the time to get out the toga that's been in your closet!
--- End quote ---
Peter, if you're frustrated that I'm just not taking you seriously, it's because I just can't take you seriously. So instead, I'm trying to find a good use for something that otherwise seems useless. I'm trying to find comedy in things that are otherwise not obviously comical.
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