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1d
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.
1d
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.
1d
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.
Feb
15
comment How are first digits of $\pi$ found?
It's almost important to note that after X operations, the first Y digits are guaranteed to be correct.
Feb
3
awarded  Nice Answer
Dec
29
awarded  Nice Answer
Dec
27
answered What parts of a pure mathematics undergraduate curriculum have been discovered since 1964?
Sep
30
awarded  Explainer
Aug
22
awarded  Notable Question
Jul
21
awarded  Yearling
Jul
2
awarded  Curious
May
13
revised Why can't you add apples and oranges, but you can multiply and divide them?
deleted 1 character in body
Mar
24
awarded  Notable Question