What is a number?
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13-08-2016, 08:38 PM
RE: What is a number?



#sigh
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16-08-2016, 11:40 AM
RE: What is a number?
(12-08-2016 11:13 AM)LostLocke Wrote:  "Novels are invented by humans, while, on most views of the subject, numbers exist whether or not humans ever happened to discover them."

Ummmm, I'm gonna go ahead here and say.... No.
It sounds like this is confusing number with quantity.
Quantities exist whether or not humans "discover" them, but the numbers are just a descriptive tool for the quantities.

LL,

Back at Uni, someone asked me " If there are stones on the beach, are there a number of stones, or is there stone?

D.
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16-08-2016, 01:59 PM
RE: What is a number?
A number can have different values...

∞ + 1 = ∞

Does 1 = 0 in this case? Or only tend to zero, which means it's no longer equal to 1 anyway?

Huh

I'm a creationist... I believe that man created God.
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16-08-2016, 02:16 PM
RE: What is a number?
(13-08-2016 08:38 PM)GirlyMan Wrote:  


Girly is the.......
ONE.... singular sensation every little step he takes!
One....... thrilling combination, every move that he makes
One........ smile and suddenly nobody else will do
You know you'll never be lonely with you-know-who

One....... moment in his presence and you can forget the rest
For the boy is second best to none, son
Oooh! Sigh! Give him your attention
Do! I really have to mention heeeee's the.....One!

Big Grin





Shakespeare's Comedy of Errors.... on Donald J. Trump:

He is deformed, crooked, old, and sere,
Ill-fac’d, worse bodied, shapeless every where;
Vicious, ungentle, foolish, blunt, unkind,
Stigmatical in making, worse in mind.
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16-08-2016, 03:34 PM
RE: What is a number?
(16-08-2016 01:59 PM)SYZ Wrote:  A number can have different values...

∞ + 1 = ∞

Does 1 = 0 in this case? Or only tend to zero, which means it's no longer equal to 1 anyway?

Huh

∞ + 1 ≠ ∞ Unless you can convince me otherwise.
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16-08-2016, 04:16 PM
RE: What is a number?
(16-08-2016 03:34 PM)Fireball Wrote:  
(16-08-2016 01:59 PM)SYZ Wrote:  A number can have different values...

∞ + 1 = ∞

Does 1 = 0 in this case? Or only tend to zero, which means it's no longer equal to 1 anyway?

Huh

∞ + 1 ≠ ∞ Unless you can convince me otherwise.

Infinity is not a number, so the expression is meaningless. You can't add or subtract numbers from infinity.
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16-08-2016, 06:54 PM (This post was last modified: 16-08-2016 07:01 PM by Reltzik.)
RE: What is a number?
Well, it's not a natural number, an integer, a rational number, a real number, or a complex number. It is, however, part of the extended versions of all those classes, and there it is a number for which arithmetic behaves a bit wonky.

Basically, you can have infinity in your number system, or conventional notions of arithmetic, but not both.

But that said, you can (sometimes) add to and subtract from infinity. The result is infinity. However, subtracting infinity from infinity is an undefined indeterminate form, so that 0 = 1 proof doesn't work.
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16-08-2016, 08:03 PM
RE: What is a number?



Insufferable know-it-all.Einstein God has a plan for us. Please stop screwing it up with your prayers.
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16-08-2016, 08:55 PM
RE: What is a number?
(16-08-2016 08:03 PM)Bucky Ball Wrote:  


So I don't know if I agree with this.
A circle is (can be) a finite and real object. A diameter can be measured, and is not undefined or only approximated. A circumference can be measured. So the idea that pi is something that is "only approximated" seems rather questionable, since pi x the diameter has a specific length, (the circumference of the specific circle in question).
Consider

Insufferable know-it-all.Einstein God has a plan for us. Please stop screwing it up with your prayers.
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17-08-2016, 01:14 AM
RE: What is a number?
(16-08-2016 08:55 PM)Bucky Ball Wrote:  
(16-08-2016 08:03 PM)Bucky Ball Wrote:  


So I don't know if I agree with this.
A circle is (can be) a finite and real object. A diameter can be measured, and is not undefined or only approximated. A circumference can be measured. So the idea that pi is something that is "only approximated" seems rather questionable, since pi x the diameter has a specific length, (the circumference of the specific circle in question).
Consider

First of all, pi is dependent on Euclidean geometry. If we have a non-euclidean geometry, then the ratio between circle and diameter is NOT pi. And anywhere we have a gravity well... which is basically everywhere in our universe... geometry is slightly off from Euclidean.

But that's not what is really being said about pi. It means that pi can only be calculated/measured to a degree of precision, rather than with complete precision. For every real-world circle, our ability to identify the length of its diameter or circumference are ALSO limited to a degree of precision. We might measure the diameter as 100cm, for example, but be off by quite a few manometers in our measurements. That means our ability to calculate pi from these real-world circles is also limited by these limits in our ability to measure. (Also, we draw imprecise circles.)

Even for theoretical circles with diameters that are defined as exact numbers, we can't calculate pi with perfect precision. Arbitrary precision, yes. However many digits we want to calculate pi out to, we can. We've sometimes get supercomputers doing ONLY this task, and they've gotten out to over 13,000,000,000,000 digits, far beyond the degree of precision that is required for any real problem. But while we can calculate it out to any degree of precision we wish, for any of these degrees of precision there WILL be error. It will be a very small error.... in pi's case, for these extreme super-computer-produced values, we have to get over a dozen TRILLION digits iin before there's ANY error... but the error will still be there. Very very small, but there. This is a problem not just for pi, but for every irrational number (and definitely for transcendental numbers look pi), because we don't even have the ability to represent and store an irrational number with complete and exact precision. That's why we always see pi written out as 3.14... or 3.14159... or so on. The ... indicates the imprecise part of pi, and no matter how precise we get, no matter how many digits we have before the ..., it is beyond human ability to calculate... or write down... the infinitely-many digits required for exact precision.
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