/sci/ - Science & Math

Let [ math] f(z) [ /math ] have a Laurent series expansion of the form <span class="math">\sum_{j=0}^{\infty}a_jz^j[\math] in <span class="math"> 0<|z|<\rho.

Would it be fair to say that this is also a power series? Can a series be both a Laurent series and a power series? I've been arguing with my prof about this for a few days. I claimed it was both in a proof and told me I couldn't and gave me no marks for it.

Similarly, if I define a polynomial p(x) = 1[\math], would it be fair to say that p(x) is both a polynomial and a number? or is it merely equal to a number?[/spoiler][/spoiler]

>>2845939
>carbon-dating involves measuring the amount of radiation left

>>1858316

Hey guys, representative from Academia reporting in from the research division of Mechanical Engineering and Materials Science. Just wanna let you know that nanotech ain't all it's cracked up to be. At least it won't be for a while. Nanofabrication alone is a bitch and a half to do right and the limit imposed by current chip technology already limits the size of electronics we can feasibly produce.

(to clarify, the reason you're seeing multi-core processors instead of dramatically faster processors is because we've reached a size limitation where chips are made so small they're at a quantum tunneling barrier: There is literally so little room between the 'wires' of a modern integrated circuit that electrons are literally teleporting to nearby 'wires' via quantum tunneling and shorting circuits. We CANNOT produce smaller chips because we're approaching a quantum barrier. There is always the possibility of developing a new style of chip (one that doesn't use electricity, for example) but sci-fi nanotech won't happen until that little hurdle is taken care of)

Of course that's not my department, that's a Physicist's problem. My department is materials and manufacture, and my AFM nanofabricator project lost funding. Fuck you too, NSF. Pic related