BlueRaja - Danny Pflughoeft
Reputation
3,954
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
19 37
Newest
 Nice Answer
Impact
~269k people reached

Jun
27
comment Easy math proofs or visual examples to make high school students enthusiastic about math
See also this question on Mathoverflow about 'Proofs without words'
Jun
3
comment Name of the highest power of 2 smaller than or equal to a given number
@Morwenn: "Bit length" works perfectly fine with Gray codes, what makes you think it doesn't? The wikipedia article even uses the equivalent term "bit width" at the top of the page.
Jun
2
comment Arc Length of Bézier Curves
A derivation of another (obviously equivalent) closed-form can be found here
May
20
comment Way to compare three numbers with an algorithm.
To account for the relative differences, divide by the mean (or median). This is called relative standard deviation
May
17
comment Are there mathematical objects that have been proved to exist but cannot be described in words?
By this same reasoning, there are some numbers that are not computable.
May
14
comment Expected return value of a recursive probabilistic function
In retrospect, a function with infinite expected value seems not-so-surprising. Take for example while(random() > 0.5) returnVal *= 2. The expected return value is $1/2 + 2/4 + 4/8 + \ldots = 1/2 + 1/2 + 1/2 + \ldots$
May
14
accepted Is concatenation of digit-strings transitive?
May
14
comment Is concatenation of digit-strings transitive?
I used this inequality to speed up the "computer simulation" I mentioned, but I didn't even think to use it in a proof - do'h! Nice job!!
May
14
comment Is concatenation of digit-strings transitive?
@Hippalectryon: Recall from where? I'm not adverse to doing research, but I wasn't able to find anything written about this problem by googling, probably because I'm using the wrong terminology.
May
14
asked Is concatenation of digit-strings transitive?
May
2
comment Does set difference distribute over set intersection?
@CKKOY The one from before the edit. The post is now "correct", but it does not actually prove what you're asking since it's not bi-directional.
May
2
comment Does set difference distribute over set intersection?
-1 The last step, $x \in A - (B \cup C) \Leftrightarrow x \in A - (B \cap C)$, is completely invalid. Take for example $A = \{1,2\}$, $B = \{1\}$, $C = \{2\}$. The "$\Leftrightarrow$" can only be an "$\Rightarrow$", which breaks the proof. @CKKOY Your book is in fact wrong, it fails for the case I just mentioned. To answer your last question, $x \in Y \cap Z \Rightarrow x \in Y \cup Z$ (because $Y \cap Z \subseteq Y \cup Z$), so your first statement implies your second.
May
2
comment Does set difference distribute over set intersection?
@MarceloUchimura No, CKKOY is correct. "$x \in A \Leftrightarrow x \in B$" implies that "$A = B$"
Apr
26
comment Curious about a made-up paradox
@Dmitry Interesting consequence of that equation: If the probability of a successful roll is exactly 50% (or better), then the gambler will always get out of debt, no matter how much his starting-debt is. Assuming he has infinite time and starting cash, that is.
Apr
5
comment Has lack of mathematical rigour killed anybody before?
This is known as the false positive paradox
Mar
31
comment Fastest way to meet, without communication, on a sphere?
"While you can determine your position relatively, [..] you cannot determine absolute 'north'" - What does this even mean? Relative to what? If it's relative to a point on the sphere, meet at that point. If it's coordinates on the sphere, move a bit and check your position again - that will tell you what direction is North.
Mar
27
comment If the earth's rotational speed increased by 2% each day starting today…what would be the difference in age 20 years from now?
This assumes the Earth's rotation gets 2% faster every rotation, not every current-rotation-speed day. It's not clear to me which the question is asking about.
Mar
23
awarded  Nice Answer
Feb
24
comment Seven line segments, with lengths no greater than 10 inches, and no shorter than 1 inch, are given.
Should that be $\leq$ and $\geq$?
Feb
23
comment What's so special about the group axioms?
There is nothing special about the group axoims, other than that there are a lot of common systems that satisfy them. By studying them, we can learn about all the systems at once.