Is infinity a squaring that has no end?

[CuriosOne]

(X^2)^2)^2)^2------->infinity???

I get this idea from meters/second^-1

Meters in this example uses a random number of 3 * 12 inches..

[swansont]

44 minutes ago, CuriosOne said:

Meters in this example uses a random number of 3 * 12 inches..

No, it doesn’t.

[ahmet]

you should (be able) to define your expession mathematically,

any set (here X)  will be infinite if

for every x element X ,there is y element X such that y>x

 

Edited November 7, 2020 by ahmet

[joigus]

An infinite power of a dimensional quantity makes no sense unless there is a constant to absorb the units to make it a sizable thing.

Otherwise, you could use a bigger unit, so that the number is zero, because it's below the unit, or a smaller unit, so that the number is infinite, because it's above the unit.

[CuriosOne]

9 hours ago, joigus said:

An infinite power of a dimensional quantity makes no sense unless there is a constant to absorb the units to make it a sizable thing.

Otherwise, you could use a bigger unit, so that the number is zero, because it's below the unit, or a smaller unit, so that the number is infinite, because it's above the unit.

How can a constant absorb the units??

Is the constant a 3 dimensional number for volume??

I hope it is, it sounds like "Summations."

10 hours ago, ahmet said:

you should (be able) to define your expession mathematically,

any set (here X)  will be infinite if

for every x element X ,there is y element X such that y>x

 

Is y and x "like terms?" 

Meaning same units? Same Base 10?

10 hours ago, swansont said:

No, it doesn’t.

It was a "theoretical" statement reference for x in my OP.

I do understand now that 1 meter =100 cm or 39.37007 inches.

And that my 3*12in = 36in + 39in = 3 × (1×1/4)

In this 1 =100cm

Are "significant digitwise" related.

For distribution I get..

25^1/2 + 1/2* 100cm = 25.50

My OP is a "Theoretical Idea."

 

 

Edited November 8, 2020 by CuriosOne

[swansont]

6 hours ago, CuriosOne said:

My OP is a "Theoretical Idea."

“Theoretical” doesn’t mean you can make up anything you please 

[ahmet]

7 hours ago, CuriosOne said:

Is y and x "like terms?" 

Meaning same units? Same Base 10?

hi, I meant and suggested that you use suitable mathematical expressions. 

telling with sentence sometimes is not sufficient for the case to be accepted or understood within mathematical approach and / or philosophy. 

recommendation: 

use and (don't leave general) theorems in basics of mathematics for instance when any function is monotone and bounded at the same time, you will not be able to say or discuss whether it would be divergent. (Because it will definitely be convergent) 

 

 

Edited November 8, 2020 by ahmet

[studiot]

19 hours ago, CuriosOne said:

(X^2)^2)^2)^2------->infinity???

I get this idea from meters/second^-1

Meters in this example uses a random number of 3 * 12 inches..

I think I understand your question.

 

Unfortunately you have confused everyone else and probably yourself with your additional remarks which are totally irrelevent.

So please start another thread inquiring about units and dimensions.

 

You are asking about what I call continued or repeated exponentiation and the American Mathematical Society calls infinite exponentials see here.

https://www.math.usm.edu/lee/BarrowInfiniteExponentials.pdf

 

This is following on from the idea of

repeated addition (the sigma symbol)

repeated product (the Pi symbol)

Continuous division

Continuous square rooting

and so on.

 

Now further information

 

A repeated process can be convergent (the result of each repeat is smaller and smaller)  or divergent (the result of each repeat is larger and large) or neither.

A repeated square root is convergent (for initial numbers greater than 1) as each time you take a square root the result is smaller than before.

A repeated square root is convergent (for initial numbers less than 1) as each time you take a square root the result is greater than before.

A repeated square root is neither convergent nor divergent (for initial number is equal to 1) as each time you take a square root the result is the same as before.

 

Can you look at your squaring process and make the same sort of analysis   - it is a worthwhile exercise for you .

 

All these processes involve infinity in some way since they could involve an infinite count of repetitions.

But only some (divergent processes) involve an infinite result.

 

For most processes it is possible to devise conditions where one of the three alternatives (for the results) holds sway for an infinite count of repetitions.

 

Does this help ?

 

[joigus]

5 hours ago, CuriosOne said:

How can a constant absorb the units??

Is the constant a 3 dimensional number for volume??

I hope it is, it sounds like "Summations."

For example, if you have a constant with units (length)^-1, you multiply it by a variable with units of length, and you get a dimensionless number.

You've started by considering a limitless power of a physical quantity. Now, that is not possible unless your model or theory has a number that 'absorbs' those dimensions.

Consider, e.g., length. If your unit of length is L. In the limit of infinite powers, you would have,

\[\left(\frac{x}{L}\right)^{\infty}=0\]

if,

\[x<L\]

But if your unit were smaller than the quantity you're considering:

\[\left(\frac{x}{L}\right)^{\infty}=\infty\]

if,

\[x>L\]

So you would need a constant to absorb those dimensions and give a sensible unit to measure in a laboratory:

\[k_{n}\left(\frac{x}{L}\right)^{n}\]

These constants normally arise because of Taylor series expansions.

It's going to take me some time to read all other comments from members.

 

45 minutes ago, studiot said:

A repeated process can be convergent (the result of each repeat is smaller and smaller)  or divergent (the result of each repeat is larger and large) or neither.

This is the key, @CuriosOne. You're getting tangled in a concept that requires the notion of convergence.

[studiot]

Edit my apologies the cut, paste and edit gremlin strikes again.

1 hour ago, studiot said:

A repeated square root is convergent (for initial numbers greater than 1) as each time you take a square root the result is smaller than before.

A repeated square root is convergent (for initial numbers less than 1) as each time you take a square root the result is greater than before.

A repeated square root is neither convergent nor divergent (for initial number is equal to 1) as each time you take a square root the result is the same as before.

This should be

A repeated square root is convergent (for initial numbers greater than 1) as each time you take a square root the result is smaller than before.

A repeated square root is also convergent (for initial numbers less than 1) although each time you take a square root the result is greater than before, the final result (1) is bounded as Ahmet said.

A repeated square root is neither convergent nor divergent (for initial number is equal to 1) as each time you take a square root the result is the same as before.

Edited November 8, 2020 by studiot

[CuriosOne]

2 hours ago, joigus said:

For example, if you have a constant with units (length)^-1, you multiply it by a variable with units of length, and you get a dimensionless number.

You've started by considering a limitless power of a physical quantity. Now, that is not possible unless your model or theory has a number that 'absorbs' those dimensions.

Consider, e.g., length. If your unit of length is L. In the limit of infinite powers, you would have,

 

(xL)∞=0

 

if,

 

x<L

 

But if your unit were smaller than the quantity you're considering:

 

(xL)∞=∞

 

if,

 

x>L

 

So you would need a constant to absorb those dimensions and give a sensible unit to measure in a laboratory:

 

kn(xL)n

 

These constants normally arise because of Taylor series expansions.

It's going to take me some time to read all other comments from members.

 

This is the key, @CuriosOne. You're getting tangled in a concept that requires the notion of convergence.

Yes, I agree totally  I should have remembered about "converging factors of 1."  But I have issues working with numbers that "tag" along in equations without these numbers popping out and introducing themselves, I speak of "round off errors" and choosing significant numbers...Its an issue for all of us "especially" in statistics..

4 hours ago, swansont said:

“Theoretical” doesn’t mean you can make up anything you please 

Of coarse not,  but my OP asks a question as it does not regard anything absolute or certain, which is funny becuase nothing in science ever is..

No one knows why enery is quantized, and how to "RECONCILE" this with the macro universe. We will never get their without bizaare thinkers, intuitives, artist or out of the box thinking.

So making up something "within" the barrier of what we know, at least to me is closer than what we "don't know." 

3 hours ago, ahmet said:

hi, I meant and suggested that you use suitable mathematical expressions. 

telling with sentence sometimes is not sufficient for the case to be accepted or understood within mathematical approach and / or philosophy. 

recommendation: 

use and (don't leave general) theorems in basics of mathematics for instance when any function is monotone and bounded at the same time, you will not be able to say or discuss whether it would be divergent. (Because it will definitely be convergent) 

 

 

I 100% agree, and I've done this before and got scrutinized becuase math is very subjective due to how numbers carry hidden information, "prime numbers" is a good example as they can be used in cryptography, squaring pi is close to the acceleration of earth 9.8 m/s^-1, and I just found that 3*10^8 m/s and 299,458,792 m/s are interchangeable and that awfull square root of x^1/2 makes no sense to me....

Atleast to me numbers mean many things all at once and im "very skeptical" about them.

Edited November 8, 2020 by CuriosOne

[joigus]

59 minutes ago, CuriosOne said:

But I have issues working with numbers that "tag" along in equations without these numbers popping out and introducing themselves, I speak of "round off errors" and choosing significant numbers...Its an issue for all of us "especially" in statistics..

I think there should be no reason in principle to be surprised that the mathematical description of a physical system requires even an infinite amount of dimensional numbers to account for its behaviour. Why not?

What is surprising is that we can get away with so much from just a limited number of universal constants.

[CuriosOne]

3 hours ago, studiot said:

I think I understand your question.

 

Unfortunately you have confused everyone else and probably yourself with your additional remarks which are totally irrelevent.

So please start another thread inquiring about units and dimensions.

 

You are asking about what I call continued or repeated exponentiation and the American Mathematical Society calls infinite exponentials see here.

https://www.math.usm.edu/lee/BarrowInfiniteExponentials.pdf

 

This is following on from the idea of

repeated addition (the sigma symbol)

repeated product (the Pi symbol)

Continuous division

Continuous square rooting

and so on.

 

Now further information

 

A repeated process can be convergent (the result of each repeat is smaller and smaller)  or divergent (the result of each repeat is larger and large) or neither.

A repeated square root is convergent (for initial numbers greater than 1) as each time you take a square root the result is smaller than before.

A repeated square root is convergent (for initial numbers less than 1) as each time you take a square root the result is greater than before.

A repeated square root is neither convergent nor divergent (for initial number is equal to 1) as each time you take a square root the result is the same as before.

 

Can you look at your squaring process and make the same sort of analysis   - it is a worthwhile exercise for you .

 

All these processes involve infinity in some way since they could involve an infinite count of repetitions.

But only some (divergent processes) involve an infinite result.

 

For most processes it is possible to devise conditions where one of the three alternatives (for the results) holds sway for an infinite count of repetitions.

 

Does this help ?

 

It helps more "than you know" thnks!

About 7 years ago, I recalled this but "forgot" how to search for the "terminology" online.

It makes just as much sense now as it did before...I truly think its a very important principle concerning "time domains" and makes things more clearer.

 

In my idea of 3*12 "The Summation" or summing up "part" are bundles of 12 to the root of 5...

That may not make any sense "right now" becuase its informal mathematics...But at this point informal and formal appear to work quite well with repetitions or loops or "for loops"..Its an oberservation 'in my field.'

15 minutes ago, joigus said:

I think there should be no reason in principle to be surprised that the mathematical description of a physical system requires even an infinite amount of dimensional numbers to account for its behaviour. Why not?

What is surprising is that we can get away with so much from just a limited number of universal constants.

What if those constant change???

By themselves??

What then?

Maybe this deserves another new topic..

Edited November 8, 2020 by CuriosOne

[joigus]

10 minutes ago, CuriosOne said:

What if those constant change???

If constants change, then they're not constants; they're variables.

[CuriosOne]

1 minute ago, joigus said:

If constants change, then they're not constants; they're variables.

Constants as G, p, h, c can be "variables" too? And the units that make these?

 

[joigus]

Universal constants don't change.

What is p?

[studiot]

17 minutes ago, CuriosOne said:

It helps more "than you know" thnks!

About 7 years ago, I recalled this but "forgot" how to search for the "terminology" online.

It makes just as much sense now as it did before...I truly think its a very important principle concerning "time domains" and makes things more clearer.

So how about attempting my question

 

3 hours ago, studiot said:

Can you look at your squaring process and make the same sort of analysis   - it is a worthwhile exercise for you .

 

What happens if you (repeatedly) square something less than 1    ?

What happens if you square (repeatedly) something greater than 1   ?

What happens if you square (repeatedly) something equal to 1   ?

[swansont]

4 hours ago, CuriosOne said:

Of coarse not,  but my OP asks a question as it does not regard anything absolute or certain, which is funny becuase nothing in science ever is..

Not being absolutely certain does not mean anything goes.

4 hours ago, CuriosOne said:

No one knows why enery is quantized, and how to "RECONCILE" this with the macro universe. We will never get their without bizaare thinkers, intuitives, artist or out of the box thinking.

Assuming that because you don’t know that nobody knows is fallacious reasoning.

 

4 hours ago, CuriosOne said:

So making up something "within" the barrier of what we know, at least to me is closer than what we "don't know." 

Making it up is still making it up.

 

 

[MigL]

6 hours ago, CuriosOne said:

I've done this before and got scrutinized becuase math is very subjective due to how numbers carry hidden information

Mathematics is the very definition of NOT subjective.
Everything is clearly defined so that everyone can understands the 'terminology'; there are no hand-waving descriptions.

Maybe, before using terms, in your posts, which you don't understand, do an on-line search for what they mean.
Again, it'll save you some embarrassment.

[CuriosOne]

10 minutes ago, MigL said:

Mathematics is the very definition of NOT subjective.
Everything is clearly defined so that everyone can understands the 'terminology'; there are no hand-waving descriptions.

Maybe, before using terms, in your posts, which you don't understand, do an on-line search for what they mean.
Again, it'll save you some embarrassment.

Your saying that numbers don't carry hidden information?? What about quantum cryptography? Decoding Reality, or the Universe..

There is a famouse value in Special Relativity in regards of "momentum" that states 0.99999999999999999 is the closest to light speed.....They should tell people its simply a ratio number of .3 cosine and I will leave it at that...

As far as accelleration is concerned, I hope we all know its simply pi ratio "confused" as a Bhor Energy Level.."Chukkles."

Also: [0.2051]^2]^2]^2 = 3.1313e-6 m/s

That is a "real" physical quantity by the way..And "the numbers change" not the variables themselves, remember water comes in 3 forms, liquid, gas and solid..

As you can see I do know math and numbers "quite well" nothing gets past me, numbers and math formulas don't make sense nor their prediction or outcomes...That's why my questions "don't get any more basic."

[joigus]

4 minutes ago, CuriosOne said:

There is a famouse value in Special Relativity in regards of "momentum" that states 0.99999999999999999 is the closest to light speed.....They should tell people its simply a ratio number of .3 cosine and I will leave it at that...

You seem to be under the impression that 0.99999999999999999... is the closest number to 1. This proves that you don't understand real numbers. That number,   0.99999999999999999... with infinitely many 9's in its digits, is exactly 1.

6 minutes ago, CuriosOne said:

As you can see I do know math and numbers "quite well" nothing gets past me, [...]

Number one seems to get past you. Why don't you accept the help of people who know more than you?

[CuriosOne]

19 minutes ago, joigus said:

You seem to be under the impression that 0.99999999999999999... is the closest number to 1. This proves that you don't understand real numbers. That number,   0.99999999999999999... with infinitely many 9's in its digits, is exactly 1.

Number one seems to get past you. Why don't you accept the help of people who know more than you?

If a number 0----> 1 is within infinity, then where is 0??? Its location?

Becuase within means "inside something" infinity must have a limit itself...I Love Grammar and Math...

I do respect the help and field of everyone.

 

Edited November 9, 2020 by CuriosOne

[joigus]

4 minutes ago, CuriosOne said:

If a number 0----> 1 is within infinity, then where is 0??? Its location?

Are you aware that you don't make any mathematical sense? Your sentences are like dadaist poems with mathematical words in them.

[CuriosOne]

1 hour ago, joigus said:

Are you aware that you don't make any mathematical sense? Your sentences are like dadaist poems with mathematical words in them.

Ok..y = x^2 and it's derivitve is y' = 2x

then shouldn't the derivitive tell you that

y' = 2x^1+2

After all x means x^1 but they don't really "make that a point" and just assume everyone justs knows that.. 

if x^1 "in regards to dy/dx, then y and x take on separate variables as [a^2+b^2]^1/2 = y^2 because 1 is a conserved natural unit, and x becomes 2 of x.....But if x--> a limit, it can never be exactly that limit, only very very very close to it...Special Relativity "at least as I see it, does the same thing...Gets close to the speed of light but not exactly.

I will wait till others accuse me of "jumping from" subject to subject, but a its how "your standard system" works apparently confusing the hell out of people whom take science and math to another level of seriousness.

By the way, Numbers and Geometry and how they "connect" are not fully understood..

Edited November 9, 2020 by CuriosOne

[joigus]

No. You don't understand mathematics, that's all.