So, I Discovered Something Rather Interesting...

[Dawn11715]

"Number of terms" as in: 

 

x + y + z has three terms (which are x, y, z).

xy + z has two terms (which are xy and z). 

oh, well than its right^^

 

just saw a0/an =...=0

[Renegade343]

Dude! Actually, wow. This is the most thought-stimulating thread I have read today.

 

As I had a moment of spare time (that's a lie, though) and I was interested in the problem (that's not a lie), I have thought a little bit about it and came up with a proof via induction.

 

http://imgur.com/iYcuTkc

 

So this relationship holds for all n in Z.

 

Yay for maths, which is prettier than the Orokin Void.

You forgot proving n = 1 is true. Without that, then assuming n = k is true is a rather big step. 

[Dhrekr]

You forgot proving n = 1 is true. Without that, then assuming n = k is true is a rather big step. 

Last paragraph, I did mention monomes (n=1, although there is no reason we couldn't start with n=0). I did claim it is trivial, and I stand by my claim.

[Renegade343]

Last paragraph, I did mention monomes (n=1, although there is no reason we couldn't start with n=0). I did claim it is trivial, and I stand by my claim.

But you do prove it instead of stating that it is trivial.

 

And the start of the set Z+ depends on different systems (and sometimes people). Some people start with 0, while others start with 1 (and to be honest, more and more people [and systems] are recognising the start of Z+ as 1). 

[Djangofett]

My brain hurts!

[Dhrekr]

But you do prove it instead of stating that it is trivial.

 

And the start of the set Z+ depends on different systems (and sometimes people). Some people start with 0, while others start with 1 (and to be honest, more and more people [and systems] are recognising the start of Z+ as 1). 

Trivial things should NEVER be proven if you are a physicist (as I am) or if you are very lazy (as I am as well).

 

However, as you have demonstrated in your first post, n = 0, n = 1 and n = 2 are true. So the demonstration is complete.

 

(Technically Z is not the set we are looking for. It is N, or N^0).

[Renegade343]

Trivial things should NEVER be proven if you are a physicist (as I am) or if you are very lazy (as I am as well).

Not really.

 

(Technically Z is not the set we are looking for. It is N, or N^0).

I did define n as the elements of Z+, for one thing (I know it works for n = 0 already, but since Z+ = {1, 2, 3, 4, ...}, that means we first prove n = 1 is true).

[Dhrekr]

Not really.

You are adorable.

 

Anyway, I'd like to thank you for the stimulating thought (and a little bit less for the nagging about not having repeated what you had already shown in your first post). Cheeryo old chap.

[Renegade343]

You are adorable.

Thing is, I am a mathematician, not a physicist. So, there is a need to prove things that are considered trivial. 

 

But I digress.