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I have the answer to your math dilemma, do you want in liner feet or metric tons?
The problem here is the you are taking the material loses of the players in the ratio. You should take their absolute material instead.
Here's what you're saying:
Position 1 : 0:0
Position 2 : 5:0 = infinite
Position 3 : 5:3
Position 4 : 10:3
Heres what you should say:
Position 1 : (Bishop+Queen):(Rook+Rook) = 12:10
Position 2 : (Bishop+Queen):(Rook) = 12:5
Position 3 : Queen:Rook = 9:5
Position 4 : Queen:null = 9:0 = infinite
Hence black shouldnt recapture with the rook as it loses his advantange from 5/12 to 0. This also matched with additive/substractive evaluations.
The fallacy is that you can't divide by zero. This is not allowed by the laws of mathematics. It doesn't give the result of "infinite;" it gives you the result of "meaningless." If you allow the expression 1/0 in algebra, it is easy to prove that 1=2. So your "ratio" of 5:0 yields no fraction and is null and void.
How's that 1=2 thing work?
@StrategicPlay: What type of math are you studying right now?
I think he means that 1/0 = infinite ; 2/0 = infinite ; therefore 1=2.
What he is saying is wrong.
Any non-zero non-infinite value divided by zero is infinite but not all infinites are the same.
You can easily say that 2/any number will always be greater than 1/the same number because 2>1. Therfore 2/0>1/0 Although that isn't an entirely accurate proof, it explains the concept nicely.
Ummm sorry, but you're wrong.
It is true that not all infinites are equal, howver, all infitinities within the same Aleph set are equal. The limit of 1/x as x approaches zero from the right is positive inifinity and is equal to the limit of 2/x as x approaches zero from the right and is equal to the limit of /x as x approaches zero from the right.
As this relates to the OP's question - the proper course would be to consider the ratio of material left on the board, if you want to work in ratios.
You all need to ask Sheldon and Leonard for help on this one.
anyway, but the mathematical problem presented here is interesting! its really worth discussion.........
nice one, wish I had said that ... I think I will ^^^^
Ummmm, even more sorry, you are both horribly wrong Kingpatzer and Hellcraft. This is surprising given your obvious talents. Possibly you have forgotten the low level stuff taught in secondary school.
Please follow the link to understand what Ricardo_Morro was referring to:
errrrr, umm... If "any number" includes negative numbers the initial statement is false. 2/-1 = -2 1/-1 = -1 -2 is not greater than -1.
So, does division by zero have the properties of division by a negative number, or a positive, considering that it is neither? Just wondering.
Division by zero is undefined in most maths. It does not = infinity (unless that's how you define it -- but it's a problematic definition that causes some rather gaping wounds in mathematical consistency).
^^^^^^^^ -- "doesn't know how to follow a link" -- OR
-- "doesn't read previous posts" --
I'll advise you to please note that I specifically stated the limit of R/x as x approaches zero, and I did not speak to division by zero specifically. Please revist any text book that discusses limits and the properties of infinity.
http://tutorial.math.lamar.edu/Classes/CalcI/TypesOfInfinity.aspx Note that infinity + infinity = infinity.
Your link simply isn't relevant to what I said precisely because I specifically am speaking to the right handed limit, and not presuming division by zero to be defined.
I'll advise you to please note that I specifically stated the limit of R/x as x approaches zero, and I did not speak to division by zero specifically. Please revist any text book that discusses limits.
Isn't relevant? I would suggest you reread the posts at least STARTING WITH THE POST BY RICARDO_MORRO which started this discussion of divide by zero, etc. to understand that you and HellCraft are so far off-base that it is laughable. None of your nonsensical tripe about limits pertains to the topic at hand - the fallacy of division by zero and its relation to the (faulty) analysis in the OP. BTW, obviously, this was part of my point, "duh, by the way, guys - you are off topic by miles".
The fact that HellCraft went astray and then you followed him is no excuse. If you don't have aything worthwhile to offer about the topic at hand, well, make your own decision I guess.
Again, what I said is accurate and correct. That you don't see it as relevant isn't really my problem.
Further, I pointed out that as the entire thing relates to the OP it's the wrong approach.
But thanks for playing.
I find your posts unpleasant to read, but I have read them.
Now, try putting in your own words the salient parts of what it is you think the link (which I read) says.
Your welcome, and, lets do it again sometime.
I'll mathematically paraphrase - take the perfectly correct equation 5x = 7x, divide both sides by x. This is known as algebra, a.k.a. do the same thing to both sides to maintain the equality.
The Result! 5 = 7
Hmmm, why did this not work out right?
Answer: We divided by zero! (since we notice that only x equal zero is a sol'n)
Can I be of any further help?
Although this tread is chockablock with Georg Cantor wannabees, the net result is much closer to transfinite mindlessness, math BA versus BS notwithstanding.
Join the "gg is arrogance" thread, at least it's still going strong after 1000+ posts.
the funny thing is that i expected an actual dilemma,instead, i got some confused Sheldon wanna be who doesn't know what he is talking about and is trying desperatly to sound deep and provocative.
A decent chess book will solve all of the OP's "actual dilemmas," whether real or (in this case) imagined. Simple enough?
And why are you trolling for math fights, and using lame TV metaphors?
Don't go dragging imaginary numbers into this too. Everybody knows they're not real.