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About this blog
My thoughts, facts, and analyses.
Entries in this blog
25
Stop saying "literally"!
"Head canon" is an oxymoron!
The Gobo monster
Carrying my pistol around town.
Statistical Analysis of Dice Rolls in Gaming
Logic and Politics, Chapter 1
Horror Movies Suck
Feeling lonely.
Grammar, "this" versus "next."
Is there really a "nerd" culture?
RPG Rants
DM: “Um, ok, I'll say that your allies are out of range.”
Archer: “Wait, if I'm out of range of his fire ball, then am I still in short range with my bow?”
Thief: “But I'm at the door trying to pick the lock, wouldn't that put me in the blast radius?”
DM: “Um, I don't know.”
Gun control does not work.
Proof that irrational numbers cannot have repeating decimals.
Multiply the number by 10m+l which gives 10m+l x = a1a2•••amam+1•••am+l . x1x2•••xn•••x1x2•••xn•••
= y + 0.x1x2•••xn•••x1x2•••xn••• Where y is some whole number. We can rearrange
10m+l x  y = 0.x1x2•••xn•••x1x2•••xn••• At this point we have reduced the problem to an assumed set of repeating decimals. We see that m or l could be 0, making for a simpler problem. Continuing, multiply by 10n 10n (10m+l x  y) = 10n 0.x1x2•••xn•••x1x2•••xn•••
= x1x2•••xn.x1x2•••xn•••
= w + 0.x1x2•••xn•••
10m+l+n x  10n y  w = 10lx  a1a2•••amam+1•••am+l On the right we have rewritten 0.x1x2•••xn••• in terms of x. In other words, we have written just the repeating part in terms of x. Note that a1a2•••amam+1•••am+l is a whole number, call it u. Algebra gives 10m+l+n x  10n y  w + u = 10lx
x = (10n y + w  u) / (10m+l+n  10l) Where the numerator and denominator on the right are both whole numbers, and therefore x is rational. This contradicts our assumption. To see this more simply, consider a case where x < 1 and does not have any decimals that are not part of the repeating series. This means m = l = y = 0, meaning all the a = 0.
Ok the super scripts don't work so I will try to fix this later.