General > General Technical Chat

Integers, Pi, and Number Lines.

<< < (11/14) > >>

TimFox:
Your use of "integer" in the above post is absurd.

tooki:

--- Quote from: Peter Taylor on July 05, 2022, 01:26:05 pm ---I'm cutting a length of pine to a rational length of 24.6 cm's, but I'm also cutting it to an integer length of 246 mm's.

The rational number 0.142857 ... recurring may repeat infinitely but it is still an integer, 1 / 7.

A "nose zing" equals 7 "whisker zings" and I want to cut my timber to a rational length of  3 / 7 th's of a "nose zing", but I'm also cutting it to an integer length of 3 "whisker zings".

A rational number refers to how an integer is represented in our number system, it doesn't refer to the type of number it is.

In LaLa Land, where they use a base 7 number system, 1 / 7 is an integer.

--- End quote ---
No, that’s not an integer. 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20, … are the first 14 positive integers in base-7.

7 isn’t even a digit in base-7, 0-6 are. (Like how base-10 is 0-9.)

TimFox:

--- Quote from: tooki on July 05, 2022, 01:38:53 pm ---
--- Quote from: Peter Taylor on July 05, 2022, 01:26:05 pm ---I'm cutting a length of pine to a rational length of 24.6 cm's, but I'm also cutting it to an integer length of 246 mm's.

The rational number 0.142857 ... recurring may repeat infinitely but it is still an integer, 1 / 7.

A "nose zing" equals 7 "whisker zings" and I want to cut my timber to a rational length of  3 / 7 th's of a "nose zing", but I'm also cutting it to an integer length of 3 "whisker zings".

A rational number refers to how an integer is represented in our number system, it doesn't refer to the type of number it is.

In LaLa Land, where they use a base 7 number system, 1 / 7 is an integer.

--- End quote ---
No, that’s not an integer. 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15, 16, 20, … are the first 14 positive integers in base-7.

7 isn’t even a digit in base-7, 0-6 are. (Like how base-10 is 0-9.)

--- End quote ---

In base-7 land, 1/7 (decimal) would be 0.1 (a septimal fraction), not an integer.
If he wants to make up new terms, he shouldn't re-define existing nouns such as "integer".

eugene:
I just experienced something that might be apropos. I had lunch at my favorite local restaurant. After enjoying the meal, the server came to the table and asked, "would you like desert?"

"Yes!" I replied. "I would like 1/4 pi radians of your delicious cherry pie!"

To which the server replied, "I'm sorry sir. I cannot serve you 1/4 pi radians of pie. Pi is an irrational number, so I cannot measure any quantity of them exactly. I can serve you 1/8 of an entire pie. Would that be okay?"

"No, thanks anyway" I said.

xrunner:
Oh we're getting weird  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

Navigation

[0] Message Index

[#] Next page

[*] Previous page

There was an error while thanking
Thanking...
Go to full version
Powered by SMFPacks Advanced Attachments Uploader Mod