- #1
- 19,464
- 10,079
What is your favorite number and why? Is it lucky? Mathematically or aesthetically beautiful? Symbolic?
jim mcnamara said:@QuantumQuest Isn't the analemma a kind of "sideways" eight as well?
OK, I'll bite. What's the significance of this number to you?fresh_42 said:Edit: And of course 4-O-9.
You know I'm simple minded enough to like their music.Mark44 said:OK, I'll bite. What's the significance of this number to you?
It makes me think of the Beach Boys song, "409 " -- http://www.bing.com/videos/search?q=she's+real+fine+my+409+beach+boys&qpvt=she's+real+fine+my+409+beach+boys&FORM=VDRE
Not sure about bringing good luck, but there's definitely convenience!SW VandeCarr said:711! It must be really lucky.
NascentOxygen said:Not sure about bringing good luck, but there's definitely convenience!
So there are no unsolvable equations in the complex numbers? I don't think so. In fact I've brought up one previously:kith said:. So [itex]i[/itex] kind of marks the end point of a long mathematical journey. (In technical terms, the complex numbers are said to be "algebraically closed".)
Viewed from a different angle, [itex]i[/itex] allows us to treat the elements of the vector space [itex]\mathbb{R}^2[/itex] as numbers (more precisely we get the field of the complex numbers). This is really cool and remarkable and the additional structure leads to many powerful and beautiful theorems in complex analysis.
jackwhirl said:Zero. It's just so dang useful.
Mort Walker fans? "Me?" 555, "The Triple Nickel."Algr said:Well, zero is my hero. :)
No polynomial equations, yes. The precise statement is given by the fundamental theorem of algebra.Algr said:So there are no unsolvable equations in the complex numbers?
That's not an equation but a set of inequalities.Algr said:Y<1
Y+X<=1
kith said:That's not an equation but a set of inequalities
No, I can't see what concerns you. The fundamental theorem of algebra tells us that every polynomial equation has a solution in the complex numbers. If we drop the constraint that our equation needs to be a polynomial equation, it is easy to construct examples which don't have a solution in the complex numbers. For example, [itex]\sin(|z|) = 2[/itex].Algr said:But it is the clearest way to describe the issue, and I'm sure you can see the intent.