Alright then, try this on for size, you BRANIACS.

An algabraic number:

www.free-definition.com/Algebraic-number.html

For example, sqrt(2) is one because it is written in algebraic form as:

1*X^2 + 0*X + (-2) = 0 .

Get it?

A trancedental number is one that is not algebraic. An example of these are pi and e.

This brings me to the question:
What about pi + e? would this be trancedental?

Why or why not? Justify your answer with a proof if you are sure. This is a question to seperate the men from the boys!

both pi and e can be written algebraicly, using sigma and infinate series. pi + e is nothing special.

This brings me to the question:
What about pi + e? would this be trancedental?

Why or why not? Justify your answer with a proof if you are sure. This is a question to seperate the men from the boys!
This is an open question.

Learn it. Know it. Live it (http://www.wsu.edu:8080/~brians/errors/your.html)

ddovala,

No, pi and e are not algebraic numbers.

What i meant was that pi and e can be expressed using sigma and infinate series. Perhaps algebraic was the wrong word: I appologize

Any real number can be expressed as an infinite series, that's nothing special.


Proving pi x e is transcendental is also an open problem that's connected to pi + e. At most one of these numbers is algebraic. These aren't easy problems, and have been open for years. There's only a handful of interesting numbers who are known to be transcendental and very few general results in this direction (Gelfond theorem). I don't think it's even known if pi+e is irrational or not.

Geez, I thought that people on this site were smarter than this. Can't even tell me if two irrational numbers are trancedental or not. Maybe there is some middle-school math bulletin board where I can get my answer. Guess we don't have any serious mathematicians on Sciforums. How dissapointing. -sigh-

I hope you're trying to be "cute".

There are many problems in mathematics that look very innocent but turn out to be real bastards. Number theory especially is filled with problems that are simple enough that the layman can understand, but have remained unsolved for hundreds of years. The question of algebraic/transcendental for many simple looking expressions is one of these.

I'm serious here. The only "cute" post on this bulliten board is a rookie (only 107 posts) trying to tell me that I'm trying to be "cute"!

Actually the other cute thing is the misuse of "your" and "you're" in the subject line, I find that kind of cute.

If Frisbinator here is so smart, perhaps he's figured out the distribution of prime numbers, or maybe HE has a proof for these and isn't sharing. But I doubt that, because if so he wouldn't partake in such childish activities as message board taunting.

Proving pi x e is transcendental is also an open problem that's connected to pi + e. At most one of these numbers is algebraic.
according to mathworld, at *least* one of them is transcendental. they might both be (and probably both are) transcendental.

it is surprising to me that the transcendentalness (?) of e+pi and e*pi are related. shows what i know, i guess

Edit:i thought shmoe said at least one is transcendental, but he said algebraic. upon rereading, i see that what he said is in line with mathworld.

it is surprising to me that the transcendentalness (?) of e+pi and e*pi are related. shows what i know, i guess


You can talk about algebraic numbers over any field, not just the rationals Q. If E is an extension field of F (meaning E is a field containing another field F), and a is in E then a is algebraic over F if it the zero of a non-zero polynomial with coefficients in E. We say E is an algebraic extension of F if every element in E is algebraic over F.

If you have a string of extension fields, K an algebraic extension of E, and E an algebraic extension field of F, then you can show K is an algebraic extension of F. Algebraic over algebraic is algebraic. This lets us build up towers of algebraic fields.

Assume pi+e and pi*e were both algebraic over Q. We can make the extension field E=Q(pi+e, pi*e)=the smallest subfield of the complex numbers containing pi+e, pi*e and Q. Then E is an algebraic extension by our assumption. e and pi are algebraic over E since they are zeros of the polynomial x²-(pi+e)*x+pi*e. So e and pi would be algebraic over Q which is false (Hermite and Lindemann respectively), so one of pi+e or pi*e must be transcendental over Q.

But what do I know, I'm just a rookie.

http://www.winternet.com/~mikelr/assets/Troller.jpg (http://www.winternet.com/~mikelr/flame29.html)

Caught any, Frisbie?

Actually the other cute thing is the misuse of "your" and "you're" in the subject line, I find that kind of cute.

If Frisbinator here is so smart, perhaps he's figured out the distribution of prime numbers, or maybe HE has a proof for these and isn't sharing. But I doubt that, because if so he wouldn't partake in such childish activities as message board taunting.

That's rather hypocritical considering your attempt to taunt me by saying that there's a grammatical error in my post, because there actually is not. I don't know what back-ass-wards country your from, but where I live, it is totally acceptable to use YOUR in place of YOU ARE. Obviously if I had a proof, I wouldn't be asking this question, now would I?

PEOPLE if your not going to post anything helpful, then just don't post at all, I'm sick of clowns like this whose only goal in life is to critisize. Who gives a rat's ass about YOUR and YOU'RE this is a math forum for crying out loud, and if your going to run around critisizing grammatical errors, there are a LOT more places on sciforums where you could do it besides THIS forum.

I have had a bad day so I am going to rant (stop reading here if you are offended by rants).

Geez, I thought that people on this site were smarter than this. Can't even tell me if two irrational numbers are trancedental or not. Maybe there is some middle-school math bulletin board where I can get my answer. Guess we don't have any serious mathematicians on Sciforums.

Who do you think you are posting a reply like this. I found this rather insulting. Maybe you are expecting too much from us?

I'm serious here. The only "cute" post on this bulliten board is a rookie (only 107 posts) trying to tell me that I'm trying to be "cute"!

Once again, why should you be so quick to judge someone's intellect based on the number of posts that they have submitted. Hardly an accurate conclusion I must say!

That's rather hypocritical considering your attempt to taunt me by saying that there's a grammatical error in my post, because there actually is not. I don't know what back-ass-wards country your from, but where I live, it is totally acceptable to use YOUR in place of YOU ARE. Obviously if I had a proof, I wouldn't be asking this question, now would I?

Sorry Frisbinator, you are wrong in this circumstance. Word2003 corrects my spelling when I type "Think your so smart?" to "Think you're so smart?" It says that this is a commonly confused grammatical error. If you wanted to use "your" then it would read "Think your intellect is so smart" or some other word instead of intellect. "Your" is a possessive pronoun and is a word which must be used in conjunction with personal adjective such as intellect or persona, etc... You're is a contraction of You are which can be used if referring directly to a person.

I would like to know the country that you live in which accepts this as proper English because I know mine does not!

PEOPLE if your not going to post anything helpful, then just don't post at all, I'm sick of clowns like this whose only goal in life is to critisize. Who gives a rat's ass about YOUR and YOU'RE this is a math forum for crying out loud, and if your going to run around critisizing grammatical errors, there are a LOT more places on sciforums where you could do it besides THIS forum.

From what I have seen in this thread it is YOU, Frisbinator, who is critisizing the members of sciforums as being, to quote: "smarter than this"; and you said this after ddovala, Lethe, James R, and schmoe had their attempts at answering your question. Since this is a forum which is open to discussion, I believe that YOU should not be posting in the first place if you are going to insult us if we get something wrong. That is kind of harsh, don't you think?

Now I believe an apology is in order, Frisbinator. - we are all waiting.... :)

"1*X^2 + 0*X + (-2) = 0"

thats wrong, it would be -2

...it is totally acceptable to use YOUR in place of YOU ARE."Your" has an entirely different meaning than "you're" or "you are".