Author Topic: Integers, Pi, and Number Lines.  (Read 8377 times)

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Offline TimFox

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Re: Integers, Pi, and Number Lines.
« Reply #50 on: July 05, 2022, 01:36:25 pm »
Your use of "integer" in the above post is absurd.
 
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Offline tooki

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Re: Integers, Pi, and Number Lines.
« Reply #51 on: July 05, 2022, 01:38:53 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.
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.)
 
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Offline TimFox

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Re: Integers, Pi, and Number Lines.
« Reply #52 on: July 05, 2022, 01:42:34 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.
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.)

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".
 
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Offline eugene

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Re: Integers, Pi, and Number Lines.
« Reply #53 on: July 05, 2022, 02:28:06 pm »
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.
« Last Edit: July 05, 2022, 02:30:12 pm by eugene »
90% of quoted statistics are fictional
 
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Online xrunner

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Re: Integers, Pi, and Number Lines.
« Reply #54 on: July 05, 2022, 02:43:31 pm »
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
« Last Edit: July 05, 2022, 05:26:37 pm by xrunner »
I told my friends I could teach them to be funny, but they all just laughed at me.
 

Offline Peter TaylorTopic starter

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Re: Integers, Pi, and Number Lines.
« Reply #55 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.
 

Offline Peter TaylorTopic starter

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Re: Integers, Pi, and Number Lines.
« Reply #56 on: July 05, 2022, 04:53:39 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

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.

 ::)
« Last Edit: July 05, 2022, 05:48:04 pm by Peter Taylor »
 

Offline eugene

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Re: Integers, Pi, and Number Lines.
« Reply #57 on: July 05, 2022, 04:55:59 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.

So now's the time to get out the toga that's been in your closet!
90% of quoted statistics are fictional
 

Offline TimFox

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Re: Integers, Pi, and Number Lines.
« Reply #58 on: July 05, 2022, 05:01:42 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.

So now's the time to get out the toga that's been in your closet!

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.
 
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Offline eugene

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Re: Integers, Pi, and Number Lines.
« Reply #59 on: July 05, 2022, 05:07:11 pm »
So now's the time to get out the toga that's been in your closet!

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.
90% of quoted statistics are fictional
 
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Offline Peter TaylorTopic starter

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Re: Integers, Pi, and Number Lines.
« Reply #60 on: July 05, 2022, 05:15:05 pm »
 :-DD

Love u all.
 

Online xrunner

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Re: Integers, Pi, and Number Lines.
« Reply #61 on: July 05, 2022, 05:32:34 pm »
A circle can be drawn to an exact (integer, or number) circumference. Cut a piece of string to that circumference, and make a circle.

A circle can be drawn 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.

But I can draw a line from the circumference to the center of the circle I just made (I must know where the center is or I could not have made the circle with an exact piece of string. So all I have to do is measure the line I just drew, and that's the diameter; not a question anymore but an answer. How can that happen?

I told my friends I could teach them to be funny, but they all just laughed at me.
 

Online IanB

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Re: Integers, Pi, and Number Lines.
« Reply #62 on: July 05, 2022, 07:05:58 pm »
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.

Absolutely it can be done. Turn a cylinder on the lathe to an exact diameter of 1 unit. Wrap a piece of cord snugly around the cylinder, and cut it where it overlaps, so that the two ends meet. You now have piece of cord exactly pi units long.
 

Offline Vtile

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Re: Integers, Pi, and Number Lines.
« Reply #63 on: July 05, 2022, 07:36:10 pm »


That is, we never, ever try to divide anything by zero there.  Instead, we can think of the process as looking at how the ratio changes as \$h\$ gets closer to zero, and extrapolate the value the ratio would be if we could calculate it at \$h = 0\$.
IIRC Newton had this concept of using something almost a zero (taste, feels and quaks like zero) as divisor when forming the concept and ideas of modern calculus. Much more intuitive, but unfortunately not mathematically rigorous.

That was fixed and reformed much later with idea of limits.   ....In sixties the duck did born again with hyper-reals.

Quack quack.
 

Offline Vtile

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Re: Integers, Pi, and Number Lines.
« Reply #64 on: July 05, 2022, 07:53:05 pm »
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.

Absolutely it can be done. Turn a cylinder on the lathe to an exact diameter of 1 unit. Wrap a piece of cord snugly around the cylinder, and cut it where it overlaps, so that the two ends meet. You now have piece of cord exactly pi units long.
Only if the string has diameter of zero.
 

Offline RJSV

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Re: Integers, Pi, and Number Lines.
« Reply #65 on: July 05, 2022, 08:18:21 pm »
Everyone:
   EITHER Fly, or get out of the Toga Closet.

(Just trying to fit in, by lookinstuupid)
 

Offline Nominal Animal

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Re: Integers, Pi, and Number Lines.
« Reply #66 on: July 05, 2022, 08:47:01 pm »
That is, we never, ever try to divide anything by zero there.  Instead, we can think of the process as looking at how the ratio changes as \$h\$ gets closer to zero, and extrapolate the value the ratio would be if we could calculate it at \$h = 0\$.
IIRC Newton had this concept of using something almost a zero (taste, feels and quaks like zero) as divisor when forming the concept and ideas of modern calculus. Much more intuitive, but unfortunately not mathematically rigorous.

That was fixed and reformed much later with idea of limits.
The way I intuitively grasped it in comprehensive school was by realizing that if one graphed the function
$$g(h) = \frac{f(x+h) - f(x)}{h}$$
(with a specific value of \$x\$, of course), then the limit \$h \to 0\$ is what \$g(0)\$ would be if it could be evaluated.  Thus, extrapolation.

If you start that by drawing a curve, picking a point on that curve, and asking the students how they'd find the tangent of that curve at that point, it's very easily graspable concept.

It becomes even more so, if you tabulate or plot the graph \$g(h)\$ with a logarithmic \$h\$ axis (\$h = 0.1, 0.01, 0.001, 0.0001, 0.00001, \dots\$).

....In sixties the duck did born again with hyper-reals.
Eww.

Well, what else can you expect from mathematicians?  I only use apply the stuff they come up with, to solve problems.
 

Offline Vtile

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Re: Integers, Pi, and Number Lines.
« Reply #67 on: July 05, 2022, 10:03:08 pm »
 

Online tggzzz

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Re: Integers, Pi, and Number Lines.
« Reply #68 on: July 05, 2022, 10:05:48 pm »
:-DD

Love u all.

I'm failing to distinguish you from a conventional troll.

Am I missing something? If so, what?
There are lies, damned lies, statistics - and ADC/DAC specs.
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Offline tooki

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Re: Integers, Pi, and Number Lines.
« Reply #69 on: July 06, 2022, 05:34:08 am »
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.
You don’t get to decide what you think the definition of a word should mean. They have established, clearly defined meanings. An integer is a number that can be written without a fractional component.

An irrational number most certainly is a number, as are non-integer rational numbers.

You need to shut the fuck up and go back to middle school (it was it primary?) math, rather than trying to tell anyone anything.
 
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