Find two real numbers that you are reasonably sure are not algebraic. Give your reason for suspecting that the value is not algebraic.

Question

anonymous · Answer

I would say prime numbers simply because there isn't an algebraic equation to express them? That would just be my guess though...

anonymous · Answer

Ah, good thought. That does make sense I will start with that.

zarkon · Answer

prime numbers (in fact all integers) are algebraic.

anonymous · Answer

Is my prof asking a trick question then?

zarkon · Answer

no

anonymous · Answer

Would numbers like pi and e be real but not algebraic?

anonymous · Answer

1 isn't algebraic?

zarkon · Answer

$\pi$ and $e$ are not algebraic

anonymous · Answer

really?  prove it!

zarkon · Answer

1 is algebraic

zarkon · Answer

all integers are algebraic

zarkon · Answer

the proofs are non trivial...pi being harder than e

anonymous · Answer

yeah i was kidding

zarkon · Answer

I know ;)

anonymous · Answer

matter of fact i don't really remember the one for $\pi$

zarkon · Answer

I'd have to look it up...I saw it once at a conference

zarkon · Answer

i believe that $$\sum_{k=1}^\infty 10^{-k!}$$ is transcendental too

zarkon · Answer

anonymous · Answer

attachment

anonymous · Answer

what about $.1234567891011121314...$

anonymous · Answer

@daniellerae9  is it clear what "transcendental" means in this context?

anonymous · Answer

Yes. I just learned what it meant the other day and forgot, transcendental numbers are just real numbers that aren't algebraic.