Starsector 0.97a is out! (02/02/24); New blog post: Simulator Enhancements (03/13/24)
Quote from: Crimson Sky Gaurdian on October 28, 2019, 11:01:46 AMQuote from: intrinsic_parity on October 28, 2019, 10:21:09 AMQuote from: Crimson Sky Gaurdian on October 28, 2019, 03:18:33 AMYes well, Maths has some stupid rules. For instance 0/0!=1, even though if you graph anything that requires it (Y=X/X, or Y=X^2 for example) it clearly does. I think you're mixing some things up. 0! = 1 so 0/0! is 0/1 = 0 but that has nothing to do with the functions you wrote as far as I can tell. Perhaps you were referring to 0/0 (no factorial) which is indeterminate. In the context of the function y = x/x, the limit as x-->0 is 1, but that's only true for that specific function.Apologies, autocorrect messing up the spacing. 0/0 != 1 is what I was trying to write.Which completely destroys the whole basis of an equation: that an equal change on both sides doesn't alter the equation.It's a stupid exception not for why it's needed, but for which part of the problem was chosen to be the exception.lim x-->0 (x/x) = 1 is still true. The equation isn't violated as x-->0.Where does doing the same thing to both sides of an equation cause the equation to be false? Also, where is an exception being chosen? The reason 0/0 is indeterminate is because you are dividing by 0, that's not a choice.
Quote from: intrinsic_parity on October 28, 2019, 10:21:09 AMQuote from: Crimson Sky Gaurdian on October 28, 2019, 03:18:33 AMYes well, Maths has some stupid rules. For instance 0/0!=1, even though if you graph anything that requires it (Y=X/X, or Y=X^2 for example) it clearly does. I think you're mixing some things up. 0! = 1 so 0/0! is 0/1 = 0 but that has nothing to do with the functions you wrote as far as I can tell. Perhaps you were referring to 0/0 (no factorial) which is indeterminate. In the context of the function y = x/x, the limit as x-->0 is 1, but that's only true for that specific function.Apologies, autocorrect messing up the spacing. 0/0 != 1 is what I was trying to write.Which completely destroys the whole basis of an equation: that an equal change on both sides doesn't alter the equation.It's a stupid exception not for why it's needed, but for which part of the problem was chosen to be the exception.
Quote from: Crimson Sky Gaurdian on October 28, 2019, 03:18:33 AMYes well, Maths has some stupid rules. For instance 0/0!=1, even though if you graph anything that requires it (Y=X/X, or Y=X^2 for example) it clearly does. I think you're mixing some things up. 0! = 1 so 0/0! is 0/1 = 0 but that has nothing to do with the functions you wrote as far as I can tell. Perhaps you were referring to 0/0 (no factorial) which is indeterminate. In the context of the function y = x/x, the limit as x-->0 is 1, but that's only true for that specific function.
Yes well, Maths has some stupid rules. For instance 0/0!=1, even though if you graph anything that requires it (Y=X/X, or Y=X^2 for example) it clearly does.
But for y = (2x^2 - x -1)/(4x^3 - 4), for x = 1, y = 0/0, but the limit approaches 1/4. So now 0/0 = 1/4 as well as 1. You can easily construct an example like this for any value of the limit and any value of x, so now 0/0 is equal to all numbers at once, which obviously can't be true. So instead we say that 0/0 is undefined, which is essentially saying that a function being 0/0 is not enough information to determine what the value of the function is. You have to take limits.
Yes, but why not have those limits be tailored to the exception, rather than the easier-but-worse option? X/X = 1, but XY/X is undefined if XY=0? Nothing breaks, and it removed a major inconsistency.Or better yet, X/X=1, but 0Y/0=YEdit: I think what I'm trying to say is the current "fix" is a hack job which is much easier solved by adding "algebraic simplification" to the front of BODMAS.
"Remember Uomoz Sector?"
The community's response to a change is inversely proportional to its importance.
BTW, it has been 112 days since last blogpost and 302 days since last update.