Given the data points (-1,2) (0,1) and (3,-4), you want to fit the best straight line, y=mx + b, through these points. given that m = -20/13, find the value of b that minimizes the error E = Ʃ ("N" on top, "i=1" on bottom) (MXi + B - Yi)^2.
This was on a test I just took for calc 1. I did the...
Exactly, its a psychological thing. Don't we all conceive of this "variable" in different ways, in a way in which each person conceptualizes it differently, but somehow conceives of it in a general way so that others can also know what one is referring to while talking about this conception...
but yet again you are saying "every type of number", and so categorizing it under a certain conception within your mind, namely all being the idea of a number (regardless of being different types) , define that conception if possible.
"The word number is just used to give it a common name."
Okay, by calling them all "numbers" you are giving them all something in common. You are saying you are only giving them a common name, but are you not also placing them under a common group, mainly being "numbers?" A complex number...
Thank you for your patience, but If i may..
You are saying that number theory is about the study of integers...which are...numbers?
So then it is the study of something which is defined to be a type of "number."
Wouldn't it seem plausible then to define number?
And may I ask why number...
I should have said "number theory will progress at an amazing rate, but far slower then it could, should it choose to continue ignoring to define certain terms."
In Joseph Dauben's book on George Cantor, his philosophy of the infinite and hsi mathematics...there is a section which talks of the first mode of generation, the second mode of generation and the principle of limitation.
Any words, any of you would like to use to describe all three of...
Edit: just saw above. Oh okay, that makes sense. I wasn't sure if there was some exact reason. Yes, i understand what we mean by "countable."
I didn't get why or where N came from for being THE set that all other sets need to be able to be mapped one-to-one to be called denumerable.
Almost...
I know the history of how set theory came about and how Cantor showed the real numbers between (0,1) were non-denumerable.
He did this by showing that they can't be put into a one-one correspondence with N (1, 2, 3...)
...So what does that really tell me? I know it tells me that the...
A finite one. A pattern in which you relate one thing to another. It stops there. Basically, can you distinguish that a pattern exists with only 2 symbols?
I'm not being smart, that's just the only way I know how to put it.
Thanks for trying though.