Recent content by rbj

there's a wikipedia page on the topic. that and the page on Planck units, maybe that can help.

all of their properties are the same. please respond to what i said, not to what i didn't say (in fact what i actually explicitly denied). i didn't say "equal". i said being that "they are not zero [and] being negatives of each other, they cannot be equal." but they are equivalent...

sorry, Halls. epic fail. replace every occurrence of ##-i## with ##i## (which has the consequence that every occurrence of ##i ## is replaced by ##-i##) and you will see your mistake.

there's always hope. he might be able to get it across to you eventually. please list (using words) a single property that ##0 + 1i## has and that ##0 - 1i## does not have. or vise versa. can you respond to the Wikipedia article pointed to several times?

a while ago i was also a Sci Adviser until i asked Greg to take me offa the list (hey DaleSpam, i think i was the first to nominate you for Sci Adviser back in 2009 or something like that). hey, listen, anyone can be clueless. and even hypocritical, in a recent cosmology thread about...

what's "GD"? "G## D#mmit"? "General Dynamics" (not much different)? sorry to be clueless.

1mile, i think the wikipedia article is clear about this. i don't know what the problem they have with it. ##-1## and ##+1## are not equivalent. one is the multiplicative identity and the other is not. in contrast, ##-i## and ##i## are qualitatively equivalent. there is not one single...

like least-squares. (i didn't even think that the least-squares method had iterations or initial conditions.)

so then we extend the concept to negative integers (what that would mean is ## -bi + bi = 0 ##) then extend it to rational ## b ##, and then hand wave to every real ##b##. makes zero sense to me. i guess. but this doesn't really say anything. my objection is to teach complex...

\frac{22}{7}, \frac{16}{5}, or \frac{7^7}{4^9}, it's all the same.

geezez, Evo. 25K posts?? i can't even count that far. maybe to the log of it.

okay. thanks.

so, lost, would you have trouble with the meaning of a+bi for b a real and positive integer? i don't know why you would have to adapt very much for that.

they are qualitatively different. only one of those two numbers are the multiplicative identity. it is no mistake to think of -i and i as qualitatively the same. every property -i has, +i also has.

yah, it's pretty much bijection. for some reason, i don't remember that term for what i would commonly call "one-to-one" or "invertible". i just wanted to include the property in the mapping that in either \mathbb{C} or \mathbb{R}^2, there were no orphaned points. "entire" appears to mean...