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/sci/ - Science & Math

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3826317 No.3826317 [Reply] [Original]

Are there transcendental numbers that CANNOT be represented as a series?

>> No.3826325

there are infinite # of transcendental numbers, so yes.

>> No.3826335

>>3826325

Could you show that they cannot be represented as a Series?

>> No.3826342

Every number can be represented by a series.

>> No.3826346

as an aside, there are uncomputable transcendental numbers.

>> No.3826350

No, no there isn't. Every number both algebraic and transcendental can be represented by a series.

>> No.3826355

>>3826335
there are infinite number, therefore it is self evident that at least one will not be representable by a series.

>> No.3826357

>>3826346
uncomputable, doesn't this necessitate that there is not a series for the number?

If there is a series, then it is computable

>> No.3826360

>>3826355


"therefore it is self evident" - Non rigorous non math major detected

please gtfo

>> No.3826366

>>3826355
> it is self evident that at least one will not be representable by a series.

What makes this case true?

Somebody's never even taken a babby math proof class.

>> No.3826367

>>3826355

5/10

>> No.3826370

find a series for one of chaitin's constants

>> No.3826372

>>3826355

see

>>3826360
>>3826366
>>3826367

KO'd

>> No.3826374

If you mean "finitely represented", yes. Else, the series that just lists their decimals is indeed a series, but you cannot in general write its nth term without using the transcendental number itself.

The number of items that you can describe with a finite amount of characters is infinite (because there is no limit on how many characters you may use, except that for each individual item, this number has to be finite), but countable (you can list them by number of characters needed, and then in lexicographical order). The number of transcendental numbers is not countable, thus there are some that cannot be described finitely (that means with series, with words, or whatever you could think of).

>> No.3826383

You can represent any real number given an infinite amount of space. However, there are infinitely many numbers which can not be represented in a finite amount of space, whether by systems of equations or infinite series or any other method.

>> No.3826391

>>3826383
>>3826374
Diagonalization hivemind.

>> No.3826430

>>3826391
Indeed. All hail to Cantor.