Let's talk Maths!

[TheOrange 0]

Fun isn't it.

 

Anyway, here's my started. I just recently watched a documentary on 'infinity'. Most of the experts on the program were pretty happy about the idea of working with 'infinity' in their calculations; one naysayer reckoned that there was such a thing as The Biggest Number after which the clock turns back to 0.

 

What perplexed me was the definition of infinity. It gets spoken about as if it was a number, but surely it's also the absence of a boundary? So when you get to old phrases like "given an infinite amount of time, a randomly typing monkey could produce the complete works of Shakespeare", is there a difference between "could" and "has"?

 

Or put another way, just because a branch of maths predict an infinite number of infinite bubble universes, does that mean they 'exist' or that there is no boundary that would prevent them from existing?

 

Or put another way again ... in an infinite universe, it's possible there could be another me out there, typing on a PowerBook, writing this silly stuff - but is this a necessary condition of the concept of infinity, or just a possible one?

 

[grungy-gonads 54]

What ARE you talking about!?

[HelperElfMissy 42]

What are you smoking?

[JA2340 16]

crack, ice or weed. washed down with shochu!

[mitchpee 10]

I think humans have too much pride in these things. What I mean by that is like religion we need ways of explaining the metaphysically supernatural. We need ways of conceptualizing and understanding what is brought before us. I don't think anyone actually understands the concept of infinity, yet we put a name to it and made it as a part of our everyday mathematics.

 

Hell the Greeks were downright scare of infinity. They could never grasp that a number which had no limit was to be used in their terminology.

[RobBright 35]

where do you think pi came from?

[JA2340 16]

Pi has a VERY well defined value.

It is the ratio of the radius of a circle to the circumference. It is so well defined it ain't funny!

 

The fact that the VALUE is a very imprecise number (ie a non repeating decimal value) has nothing to do with whether the definition is precise.

OTOH, infinity has no value, because as soon as you give it a value, one can always add "1" to that value and it is still bigger than the earlier value.

[mitchpee 10]

hence the reason it is not able to be conceptualized by man.

[JA2340 16]

Yup!

[RobBright 35]

Originally Posted By: JA

Pi has a VERY well defined value.
It is the ratio of the radius of a circle to the circumference. It is so well defined it ain't funny!

yes the ratio, which is defined as pi but not as a number though?

[js 0]

Complicated matter - both ends of the spectrum had a philosophical basis, both 0 and Infinity.

 

The Indians were perhaps the first to properly discuss this, and are generally associated with the creation of 0 as a 'real' number. (There's an interesting TV documentary on this)

 

(Funny how the consequences of ones history can ripple through time - modern India is notable for its computer science achievements, though without the 'discovery' of 0 some 2000 years ago we wouldn't have the binary language or computers.)

 

 

From my early spherical trigonometry (survey) math days, Pi is a ratio most often expressed as a number in decimal form (3.141, etc). It can be represented in different numbering systems too (binary, etc).

[Jynxx 4]

What "aint funny" is that people are just using the words and stringing them and think they are talking Math or Quantum physics, etc.

Maths have very well defined values, 0, ∞, π whichever...

When a number goes to infinity, or a number goes infinitely close to 0 , that's just what it means. Nothing abstract about that.

Maths is conceptual, and it can get abstract. But you don't make things abstract when the basic definition is clear. It's like saying, what is the distance between 0 and 1, or 1 and 2 when I say that a number can infinitely go small close to 0. Then someone might say- geez, then the distance between those numbers is infinite. ??? You can't do that.

One can say "The existence of non-existence" sounds philosophical?

Zero is a quantity, hence as quantity, it exists. Nothing philosophical about that. But, when one starts stringing words to say to the effect of, "Zero is nothing there as quantity, but it's real and exsist, hence that is existence of non- existence" Do you get my point?

 

Let's talk imaginary numbers for example. Square root of minus one. The number multiplied by itself becomes minus one. Cool huh? It doesn't exist, it's imaginary? ... get into electronics for example and it makes perfect sense. As a matter of fact, it seems to exist.

I always wondered why skeptics don't take up issues on this. Here is a ghost number !

Here, we have conceptual tool that works, it can be experimentally proven (can it? it looks like but maybe I'm wrong and it's a illusion. Some dope said god don't play dice with the universe).

Since it is conceptual, we can say that comes from awareness, so the study in maths is looking at the history of human awareness. I'd say we are standing on the shoulder of giants when it comes to maths.

 

I don't know what to talk about whether it's gonna be pure or applied, but If it's gonna be coffee shop talk, that's that ...

 

[RobBright 35]

Usually I can follow your posts jynxx but that is all over the shop mate.

[JA2340 16]

Originally Posted By: SubZero

From my early spherical trigonometry (survey) math days, Pi is a ratio most often expressed as a number in decimal form (3.141, etc). It can be represented in different numbering systems too (binary, etc).

I think the confusion with PI comes about because it is non-repeating as far as it has been calculated (which is into the range of, I think, hundreds of decimal places). So, as a decimal number, it is not easy to "define" the exact value, but the ratio is very well defined.

[RobBright 35]

Pi is defined as a ratio, yet the numerical value, at the moment, is infinity and has no recurring numerical value.

 

Also numbers have various types of forms - real numbers, rational or irrational numbers, natural numbers etc. Infinity, from my A-level maths and uni degree, was classified as an irrational number.

 

The question should be why do we have infinity? Why can there not be a finite boundary?

[JA2340 16]

Originally Posted By: RobBright

Pi is defined as a ratio, yet the numerical value, at the moment, is infinity and has no recurring numerical value.

Not sure that's accurate. In fact the VALUE is known to a fair degree of accuracy, but there is no point at which the value exhibits repeating decimal places, so the decimal value is not fully defined. That's a lot different to infinity!

There may be an infinite number of decimal places to which PI does not repeat, but that's not equal to infinity!

Originally Posted By: Wikipedia

π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.141593 in the usual decimal notation (see the table for its representation in some other bases). The constant is also known as Archimedes Constant, although this name is rather uncommon in modern, western, English-speaking contexts. Many formulae from mathematics, science, and engineering involve π, which is one of the most important mathematical and physical constants.[5]

π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.

Reference

[Jynxx 4]

Rob,

what can't you understand when I am trying show you that Maths is a language that has clear definitions, and it's annoying to talk to people who ignores that and puts their own meaning on to it. JA is trying to tell you that you are doing that, while you are using the term infinity to describe a irrational number.

Their is nothing conceptual about ∞, π . We can talk maths in pure maths or applied maths. We are not talking maths when people talk about philosophical implications, or science fiction. It's entertaining, and certainly we can talk about the history of math and human thought. But, I'd draw a line talking to people who thinks Star Trek is physics, or people who says they understand quantum physics just because they read a few books written for laymen and doesn't even understand calculus.

Shoot, me, we aren't even through with the definition of Real, Imaginary, Whole, Natural, Rational numbers. Are we at this level trying to understand maths terms? Looks like it when I see ...

Originally Posted By: RobBright

The question should be why do we have infinity? Why can there not be a finite boundary?

 

boundary means something else in maths.

 

To answer your question,

example : some equations have infinitely many derivatives. Smooth functions. etc.

[RobBright 35]

Originally Posted By: Jynxx

boundary means something else in maths.

To answer your question,
example : some equations have infinitely many derivatives. Smooth functions. etc.

a boundary is a border that is encloses an area or space, ie a triangle or circle, hence why we have pi x r^2 for the area of a circle or width x length = area of a square.

that isn't the question I asked.

the question I asked, is why do we have infinity? we can there not be a finite boundary of numbers ? that last part was added to make it clearer.

[Jynxx 4]

Actually, I thought about an easier explanation.

Think about a number infinitely close to zero. Can be written x âž 0

that's : 0.000000...infinite numbers of 0 followed by ...0001 and it still isn't 0.

Why do we need that? Because we cannot divide by zero, so we can only take a limit. Remember? L'Hopital's rule?

 

Also,

many students INCORRECTLY conclude that ∞/∞ is equal to 1 , or that the limit does not exist. ∞ minus ∞ is not zero. These are indeterminate forms that we avoid so that we can take a limit.

[RobBright 35]

but surely saying that 0.000...00001 isn't 0 is equivalent to saying that 0.9999999..............9999 doesn't = 1 right?

[Jynxx 4]

Does that give you some idea of what you want to describe as "finite boundary of numbers"

Still I say, that you are stringing words together. it can mean all thoughts of things.

Words means different things to different people. In the field of science, say fracture and it means different things in metallurgy (material science) from medical science.

Even in maths, there's geometrics, topology, and boundary solutions and parameter in calculus.

I don't understsnd what you are getting at ...

 

[RobBright 35]

did you answer my question?

 

Originally Posted By: Jynxx

Still I say, that you are stringing words together. it can mean all thoughts of things.

 

et tu Jynxx?

[Jynxx 4]

Originally Posted By: RobBright

but surely saying that 0.000...00001 isn't 0 is equivalent to saying that 0.9999999..............9999 doesn't = 1 right?

You mean this is a question?
What's the point?
infinitely recurring numbers, 0.99999 put a dot on top of the last 9 to discribe that.
and comparing 0.0000000.... ending with a 1 in the end is not a recurring number if you what to argue that way.
But the point is xâž1, and xâž0 is different because we are talking about application that shows it is usable.
Doesn't my explanation make you click that a number infinitely close to zero (which is a number you can divide by) is different to zero (which is a number you cannot divide by) is tool to avoid this indeterminate situation.

[RobBright 35]

because 0.9 with the dot above has been proven to equal 1, so in regards to that then 0.000......0001 in turn = 0?

 

Infintely recurring numbers are known as irrational numbers as they follow a pattern.

[RobBright 35]

1/3 = 0.3333 with dot above right?

 

3/3 = 1 right?

 

yet 0.33 with dot above x 3 equals 0.99 with dot above.