Use pigeonhole principle
Reference:
http://en.wikipedia.org/wiki/Pigeonhole_principle
http://stackoverflow.com/questions/1586858/find-the-smallest-integer-not-in-a-list
Showing posts with label Math. Show all posts
Showing posts with label Math. Show all posts
Sunday, October 18, 2009
Tuesday, July 21, 2009
Math, Feeling The Logarithm (Concents)
Remember the basic fact: y = a^x <==> loga y = x
translate to "how many times of multiplication of a" can get you y?
for example, log264 = 6
logx(1/8) = 3,
then x = ?
x^3 = 1/8, so x = 1/2
log (1/16) x = -0.75,
then x = ?
(1/16)^(-3/4)
= [(1/2)^4]^(-3/4) note: (a^n)^m = a^(n*m)
= (1/2)^(-3)
= 1/[(1/2)^(3)] note: reciprocal for negative exponent
= 1/(1/8)
= 8
Review p.141 yellow book, see the graph, feel the grow of log function.
logaXY = logaX + logaY
loga(X/Y) = logaX - logaY
logaX^n = n logaX
loga^nX = (1/n)logaX
a^(logaX) = X
translate to "how many times of multiplication of a" can get you y?
for example, log264 = 6
logx(1/8) = 3,
then x = ?
x^3 = 1/8, so x = 1/2
log (1/16) x = -0.75,
then x = ?
(1/16)^(-3/4)
= [(1/2)^4]^(-3/4) note: (a^n)^m = a^(n*m)
= (1/2)^(-3)
= 1/[(1/2)^(3)] note: reciprocal for negative exponent
= 1/(1/8)
= 8
Review p.141 yellow book, see the graph, feel the grow of log function.
logaXY = logaX + logaY
loga(X/Y) = logaX - logaY
logaX^n = n logaX
loga^nX = (1/n)logaX
a^(logaX) = X
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