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Mr. Astrophysicist

Are mathematical constants equivalent to Infinity?

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While some say that pi goes on and is infinite, much like e (Euler's Number), but not square root of 2, and other mathematical sums as it may stop, are they similar to infinity? I know that infinity cannot be counted or regarded as a number, but what if we regard infinity as or equivalent to 9999999999999999999999999999999.... So on, and so forth. Or for you brilliant mathematicians prefer to this formula:

∞ = 9999999999999999999999999999999999999999999999...

So what do you think? Guys, what are you opinions of infinity and mathematical constants? Are they equivalent to quantities, as they both go on?

(Hard eh?)

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While some say that pi goes on and is infinite, much like e (Euler's Number), but not square root of 2, and other mathematical sums as it may stop, are they similar to infinity?

 

These numbers are all irrational (including the square root of 2) which means that their representation is an endless, non-repeating series of digits.

 

They are NOT infinite. They are all small numbers.

 

Note that there is more than one infinity. There are infinitely more real numbers than there are integers, for example.

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Are mathematical constants equivalent to Infinity?
Started by Jordyn Rahizel, Today, 04:54 PM

 

 

 

 

Of course not.

 

Is infinity a constant?

 

What does adding 100 to infinity make?

 

is (9recurring ) + 100 = (9recurring) ?

 

Infinity is not a real number or an integer, 9 recurring is and obey all the rules of integers and ral numbers.

 

There are number systems which include an infinity, but not the real numbers or the integers.

Edited by studiot

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Of course not.

 

Is infinity a constant?

 

What does adding 100 to infinity make?

 

is (9recurring ) + 100 = (9recurring) ?

 

Infinity is not a real number or an integer, 9 recurring is and obey all the rules of integers and ral numbers.

 

There are number systems which include an infinity, but not the real numbers or the integers.

Did you have infinity if you can add 100 to it?

You can add a hundred more 9s as in 999999999 ...... to a recurring series.

Edited by Robittybob1

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One of the properties of infinity is adding any real number to it still makes infinity, or if you like subtracting any real number still makes infinity.

 

Neither of these are properties of (9recurring).

Edited by studiot

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Did you have infinity if you can add 100 to it?

You can add a hundred more 9s as in 999999999 ...... to a recurring series.

 

Adding 100 more 9s is not the same as adding 100 (it is more like multiplying by 10101).

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Adding 100 more 9s is not the same as adding 100 (it is more like multiplying by 10101).

It was just my bad maths.

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Besides, just because the representation of a number in decimal has infinite non-repeating non-patterned digits, doesn't mean they all do. Instead of decimal (base 10), if we use base [math]\pi[/math], [math]\pi_{10} = 10_{\pi}[/math] (pi in base 10, is represented by 10 in base pi). And [math]1_{10}[/math] has an infinite non-repeating non-patterned representation in base [math]\pi[/math].

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To add another wrinkle, every non-zero terminating decimal actually has two decimal representations, one of which ends in infinitely many 9's (or infinitely many of whatever the highest digit is in other bases). For instance (and most famously), 1 = 0.999.... Other examples include 3.578 = 3.577999, 100.23451 = 100.23450999..., 720934750234567.124 = 720934750234567.123999..., etc. So every number can be expressed as having infinitely many non-zero digits, but certainly not every number is similar to infinity (in fact, no real number is, as others have said).

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One of the properties of infinity is adding any real number to it still makes infinity, or if you like subtracting any real number still makes infinity.

 

Neither of these are properties of (9recurring).

 

You are interpreting the definition of infinity on entirely maths based assumptions. MrAstrophysicist's question, if attention is given to the 'quantities' reference, is intended to examine whether mathematical indivisibles are reflected in physics as phenomenal constants, ie; the fact that the golden mean is observed in nature reflects the condition that there is not a mechanism of entropy that will allow a sunflower to position it's seeds in a different pattern. As a question of nucleosynthesis and gauge forces this implies that irrational numbers define infinite boundaries where whole numbers define the human FoR and the context math's has been developed from.

 

Perhaps the question is better examined in terms that define mass regulation rather than from a purely mathematical position?

Edited by GeneralDadmission

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You are interpreting the definition of infinity on entirely maths based assumptions.

Which has to be the correct way. How it relates to concepts in nature is a separate question, however, applications of mathematical ideas can of course lead to refinements of the original ideas.

 

 

 

 

Anyway, we should consider the expression bellow and this is what we would like to mean by '999r'. (Not to be confused with 0.999r or any recurring decimal.)

 

[math] 999r \: ``="9 \sum_{n=0}^{\infty}10^{n}[/math].

 

This is clearly a divergent series. It does not have a well defined value.

 

However a better way to look at this is as a limit and consider

 

[math]999r = 9 \lim_{k \rightarrow \infty} \sum_{n=0}^{k}10^{n}[/math],

 

this limit is infinity. So, being careful with what we mean by '999r', either it is infinity or simply meaningless. Note there is noting special about 9 here. I could equally have considered any natural number.

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You are interpreting the definition of infinity on entirely maths based assumptions. MrAstrophysicist's question, if attention is given to the 'quantities' reference, is intended to examine whether mathematical indivisibles are reflected in physics as phenomenal constants, ie; the fact that the golden mean is observed in nature reflects the condition that there is not a mechanism of entropy that will allow a sunflower to position it's seeds in a different pattern. As a question of nucleosynthesis and gauge forces this implies that irrational numbers define infinite boundaries where whole numbers define the human FoR and the context math's has been developed from.

 

Perhaps the question is better examined in terms that define mass regulation rather than from a purely mathematical position?

 

!

Moderator Note

Since it's posted in the math section, no, it is not better to discuss this in terms of physics. It's a math question. Please discuss this in the context of the OP.

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!

Moderator Note

Since it's posted in the math section, no, it is not better to discuss this in terms of physics. It's a math question. Please discuss this in the context of the OP.

 

I indicated that our construction of math around whole numbers has defined mathematics. Quantity is defined by physics and is expressed by irrational numbers. I did not suggest discussing particles but defining what is a whole number outside what we want from it. Get your facts straight and you'll stop looking like a ponce.

Edited by GeneralDadmission

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!

Moderator Note

 

GeneralDadmission

 

Don't respond to modnotes (including this one) in the thread- in future you risk having your whole post hidden.

 

Don't insult other members.

 

And Stick to the topic - and keep to the correct forum; this means not crow-barring your current pet theory into every answer.

 

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You are interpreting the definition of infinity on entirely maths based assumptions. MrAstrophysicist's question, if attention is given to the 'quantities' reference, is intended to examine whether mathematical indivisibles are reflected in physics as phenomenal constants, ie; the fact that the golden mean is observed in nature reflects the condition that there is not a mechanism of entropy that will allow a sunflower to position it's seeds in a different pattern.

 

Sunflowers always develop their seeds in the same pattern (no surprises there; it is defined by their genetics). But note that it is only approximately a fibonacci sequence. Also there are other plants which do not organise there seeds in this sort of pattern. So this doesn't really tell us anything about the world.

 

And it still has nothing to do with infinity.

I indicated that our construction of math around whole numbers has defined mathematics.

 

Maths deals with real numbers and well as other more complex structures, not just integers.

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Sunflowers always develop their seeds in the same pattern (no surprises there; it is defined by their genetics). But note that it is only approximately a fibonacci sequence. Also there are other plants which do not organise there seeds in this sort of pattern. So this doesn't really tell us anything about the world.

 

 

 

And all systems in nature are systems of entropy.

 

 

 

And it still has nothing to do with infinity.

 

Maths deals with real numbers and well as other more complex structures, not just integers.

 

And how does the mathematical definition of infinity have a functional description of nature in it? I did not state that the golden mean is related to infinity. I stated that whole numbers are better defined by nature than by our requirement to see an apple as 1 apple.

Edited by GeneralDadmission

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And all systems in nature are systems of entropy.

 

Which appears to be irrelevant to the OP.

 

And how does the mathematical definition of infinity have a functional description of nature in it?

 

It doesn't. But the thread was about infinity.

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Which appears to be irrelevant to the OP.

 

 

It doesn't. But the thread was about infinity.

 

Perhaps I read too much into his intentions I thought he was seeking to identify irrational numbers as sets of infinity.

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lim(x to inf) of x = inf

 

lim(x to inf) of 2x = inf

 

but ( lim(x to inf) of x ) / ( lim(x to inf) of 2x = inf ) = 0.5

 

inf/inf can be equal to any number, so as you can see it does not function like any "constant". Infinite is in a league of its own.

Edited by CasualKilla

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Sunflowers always develop their seeds in the same pattern (no surprises there; it is defined by their genetics). But note that it is only approximately a fibonacci sequence. Also there are other plants which do not organise there seeds in this sort of pattern. So this doesn't really tell us anything about the world.

...

Well, the general is court-marshaled but I have information to share on your point. All plants develop their stems and leaves in patterns of Fibonacci numbers. This phenomena is called phyllotaxis. It turns out this does tell us something about the world.

 

...

Phyllotaxis and mathematics

Physical models of phyllotaxis date back to Airy's experiment of packing hard spheres. Gerrit van Iterson diagrammed grids imagined on a cylinder (Rhombic Lattices).[8] Douady et al. showed that phyllotactic patterns emerge as self-organizing processes in dynamic systems.[9] In 1991, Levitov proposed that lowest energy configurations of repulsive particles in cylindrical geometries reproduce the spirals of botanical phyllotaxis.[10] More recently, Nisoli et al. (2009) showed that to be true by constructing a "magnetic cactus" made of magnetic dipoles mounted on bearings stacked along a "stem".[11][12] They demonstrated that these interacting particles can access novel dynamical phenomena beyond what botany yields: a "Dynamical Phyllotaxis" family of non local topological solitons emerge in the nonlinear regime of these systems, as well as purely classical rotons and maxons in the spectrum of linear excitations.

 

Close packing of spheres generates a dodecahedral tessellation with pentaprismic faces. Pentaprismic symmetry is related to the Fibonacci series and the golden section of classical geometry.[13] ...

As the Fibonacci sequence is a countably infinite set, we have some connection to the OP in this.

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Well, the general is court-marshaled but I have information to share on your point. All plants develop their stems and leaves in patterns of Fibonacci numbers. This phenomena is called phyllotaxis. It turns out this does tell us something about the world.

 

Interesting.

 

It is a good job I specified seeds, then! I was specifically thinking of lotus seeds. So after reading this I thought I should check and the first seed pod I looked at (on the web) had two rings of 8 and 13 seeds. But that turned out to be an exception, none of the others had more than 1 number from the Fibonacci series (and many had none).

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ajb

Anyway, we should consider the expression bellow and this is what we would like to mean by '999r'. (Not to be confused with 0.999r or any recurring decimal.)

 

73e86f74724d5442f0a5f720a9dc1281-1.png.

 

This is clearly a divergent series. It does not have a well defined value.

 

However a better way to look at this is as a limit and consider

 

9bc6b0806b07084d2bd698de9c50fbee-1.png,

 

this limit is infinity. So, being careful with what we mean by '999r', either it is infinity or simply meaningless. Note there is noting special about 9 here. I could equally have considered any natural number.

 

 

Not to contradict ajb, but to add:

 

It should be noted that the value of something may or may not be equal to its limit, if it only has one limit.

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Infinity is generally ambiguous, but I've come up with a theory that possibly define it's numbers. So, the value of Infinity is:

Infinity = 9999999999999999999999999...

So on, so forth. Since 9 is the largest of all the numbers 1 - 10 (except for 10, which has 2 digits), or so to say 9 is the biggest of all 1 digit numbers. Since Infinity is not affected by numbers, this somewhat similar mathematical constant is not affected by numbers. Ergo:

9999999999... + 1 = 99999999...

It may seem rather unusual, so imagine that infinity is not a constant value. What do you guys think?

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The only real issue with infinity is that it obeys different rules from real numbers.

 

Therefore you require different mathematics to handle it

 

Folks get into difficulty because they keep trying to make it follw the normal rules of number and then find inconsistencies when it doesn't.

 

Use the appropriate maths and all will be fine.

 

Note this is not to say we know everything about it.

That would be crass arrogance.

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There is infinitely many numerical systems, and decimal system is just one of them..

http://en.wikipedia.org/wiki/Numeral_system

 

You, in your ignorance, are giving decimal system preferred place.

 

Why don't you define infinity as binary %11111.....1111 infinitely many repeated?

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