Transcendental numbers

Al-Allo · 2014-08-03 12:06:27

Hi,

I was wondering, what are Transcendental numbers ? I've never heard of such type of numbers. Thank you!

Last edited by Al-Allo (2014-08-03 12:06:47)

bobbym · 2014-08-03 13:14:18

Hi;

You have heard of them:

Transcendental numbers are numbers (possibly complex) that cannot be the root of a nonzero polynomial with rational coefficients (i.e., not an algebraic number). Examples of such numbers are pi and e .

Definitions vary but the above is the one I like.

Agnishom · 2014-08-03 20:03:04

Are they meaningful?

bobbym · 2014-08-03 20:05:35

My opinion would be no but I am not Jean.

Bob · 2014-08-03 22:16:54

Oh! Now I feel sorry for transcendental numbers. Don't they have as much right to be meaningful as all the other numbers ? Surely, all numbers are created equal* and such discrimination against one set is number_racist.

* By which I mean have equal status; not equal in value ... that would be silly.

Bob

bobbym · 2014-08-03 23:52:10

Mr. Chattopadhyay has been trying to prove the meaningfulness of 10^10 while Jean Dieudonne disagrees. For my part it is not a case of discrimination but rather a case of some numbers being exalted unfairly. Why are e and pi given lofty titles and the √ 2 is called irrational? Look at the case of the unfair treatment of the number 1. Oh it is okay for e to show its feathers and say I am equal to 2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427... What happens when the number 1 proudly displays itself as .999...? People get mad and refuse to believe it.

I think the difference between Agnishom and myself in this is that while he chooses to analyze Jean's comments I just do what I always do when confronted by concepts I can not understand. I just ignore them and hope they will go away.

Agnishom · 2014-08-04 00:27:38

bob bundy wrote:

Oh! Now I feel sorry for transcendental numbers. Don't they have as much right to be meaningful as all the other numbers ? Surely, all numbers are created equal* and such discrimination against one set is number_racist.
* By which I mean have equal status; not equal in value ... that would be silly.
Bob

I fully agree with your point. The king of combinatorics from Vegas does not.

Argument here: http://www.mathisfunforum.com/viewtopic.php?pid=326916#p326916

Agnishom · 2014-08-04 00:33:20

bobbym wrote:

What happens when the number 1 proudly displays itself as .999...? People get mad and refuse to believe it.

It is people's problem, not 1's. Not even yours or mine.

bobbym · 2014-08-04 00:35:28

Nope, it never was my intention to validate or condemn his viewpoint. If I have given the impression that I am in support of his ideas then I am sorry.

The king of combinatorics from Vegas does not.

The person who said that was being snarky and downright mean. Anyways, in the spirit of the great Paul Nahin EM makes combinatorics problems easy.

Bob · 2014-08-04 04:20:19

OK. I have looked at the small subset of that thread concerning Dieudonne and the meaning of three. Life is too short for me to read all 8 pages of the thread so I apologise if I am repeating anything said there.

He may be a brilliant mathematician but I still have to disagree with his logic. He says that 3 has a meaning for him because he can see 3 apples. (Thank you for supplying a picture just in case I cannot visualise this. ) But he does not see 3. He sees 3 apples. These are not the same thing. You cannot 'see' any number. Numbers are just abstract concepts that we use to make models of the real world. In the model as it relates to apples, if you have 3 apples and someone gives you another 2 apples, then you have 5 apples. That's how useful the model is. But those number concepts don't exist on their own except as part of a mathematical model. And the model treats all numbers equally (as defined in my earlier post); so, either they are all meaningful, or none are.

As it happens I don't have too much difficulty visualising something (not apples this time) that there could be 10^10 of. I'm picturing 141 bankers, each charged with bringing some cash in to pay off the Uk National Debt. (http://www.nationaldebtclock.co.uk/) £10^10 should just about do it. Thanks guys. [note: it is impossible to give the exact figure since it is constantly changing but you get the idea.] If you want a picture you'll have to wait while I count up all those £s. Could be some time.

Bob

Agnishom · 2014-08-04 04:28:12

That is an excellent argument, bob!

What is your opinion on infinite cardinals like

?

I am not well versed in economics but is the sum total of all the debts of the countries zero? If not, where is the debt coming from?

Last edited by Agnishom (2014-08-04 04:36:31)

Bob · 2014-08-04 04:35:23

If we can use them, then they have meaning. And they are used.

Just trying to get a free image of some money. I may have to photo some of my own.

Bob

Agnishom · 2014-08-04 04:37:45

Where are they used?

I am not well versed in economics but is the sum total of all the debts of the countries zero? If not, where is the debt coming from?

Bob · 2014-08-04 04:49:09

Research Cantor.

Is the sum total of all debt zero? Excellent question. But I do not know the answer. I shall log off and give it some thought.

Bob

Agnishom · 2014-08-04 04:55:13

Dr. Soumitra Sengupta, department of theoretical physics wrote:

Galileo wrote:
A statement is scientific iff it is possible to design an experiment or a thought experiment that can attempt to disprove it.

Is there any experiment to show that 10^10 is meaningful?

Bob · 2014-08-04 06:11:56

First you would need to define meaningful.

Bob

Bob · 2014-08-04 08:38:21

Agnishom wrote:

I am not well versed in economics but is the sum total of all the debts of the countries zero? If not, where is the debt coming from?

I found this:

http://www.theguardian.com/notesandquer … 54,00.html

and started out, optimistically understanding it. Ar ha! the answer does appear to be sum(debt) = zero. But, the more I read, the less I knew. In the end I was back where I started. This is why I prefer maths to economics.

Edit: I searched on and found this:

http://www.economicshelp.org/blog/334/u … onal-debt/

This makes more sense but the figure is not the one on the clock. It seems the largest share of the debt is owed to people in other countries. Oh help!

If I cannot sleep tonight, it will be your fault!

Bob

Agnishom · 2014-08-04 12:13:29

Hi bob;

I am sorry. How did the night go?

Bob · 2014-08-04 19:23:51

hi Agnishom,

I slept well, thanks. Now to work on that picture. I've got to 1000 so far, but I hope to continue exponentially, so it shouldn't take long.

Bob

Agnishom · 2014-08-04 19:43:38

You should automate that with a script.

I did not find any use of Infinite cardinals

Last edited by Agnishom (2014-08-04 19:44:06)

Bob · 2014-08-04 19:56:04

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

Bob

Agnishom · 2014-08-04 19:57:49

There are no uses of infinite cardinals in that page

Bob · 2014-08-04 21:34:07

In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets.

That sounds like 'infinite cardinals' to me, so I assume your objection is that it has no use. Frankly, I'm shocked that a scientist like yourself would try to argue that 'pure' research is not useful. As I'm fond of saying, prime number theory was thought to have no use outside of pure maths. Then they invented the internet, and where would we be without prime number encryption ?

So who can say that any branch of maths is not useful ? The whole of real number theory is based on the idea of number density and that is based on cardinality. If you start downgrading topics because you think they are not useful, watch out, for the whole 'house of cards' may come tumbling down. It's not compulsory that you, personally, have to be interested, in order for a theory to exist and, to someone, be useful.

Bob

Agnishom · 2014-08-05 00:22:12

I am sorry. I do not mean to downgrade it. I only wish to know if it is useful.

Also, much of it is bobbym's idea, not mine.

Last edited by Agnishom (2014-08-05 00:22:46)

Bob · 2014-08-05 00:42:48

hi Agnishom,

No apology necessary. There is no absolute mathematics authority that decides what topics may be studied nor which are valid. If you want you may study a topic. For me, I follow that which is interesting for me. I find it amusing that

and yet these sets have the same cardinality. For me that is enough to make it a useful and meaningful study.

Bob

Math Is Fun Forum

#1 2014-08-03 12:06:27

Transcendental numbers

#2 2014-08-03 13:14:18

Re: Transcendental numbers

#3 2014-08-03 20:03:04

Re: Transcendental numbers

#4 2014-08-03 20:05:35

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#5 2014-08-03 22:16:54

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#6 2014-08-03 23:52:10

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#7 2014-08-04 00:27:38

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#8 2014-08-04 00:33:20

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#9 2014-08-04 00:35:28

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#10 2014-08-04 04:20:19

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#11 2014-08-04 04:28:12

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#13 2014-08-04 04:37:45

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#14 2014-08-04 04:49:09

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#18 2014-08-04 12:13:29

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#25 2014-08-05 00:42:48

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