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Oct
25
revised Another way of counting probability
Corrected for the condition that at least one number has to be chosen
Oct
25
comment Another way of counting probability
@paw88789: Ah right, I overlooked that condition. But the claim that all possible sets are chosen with equal probability should still be sufficient. I'll rework the answer.
Oct
25
answered Another way of counting probability
Oct
25
answered Sequences with Infinite Number of Accumulation Points
Oct
25
comment Relatively tight upper and lower bounds for surreal numbers
@NormalHuman: Do you have a bot to add those comments, or how did you manage to add it so quickly after posting?
Oct
25
revised Relatively tight upper and lower bounds for surreal numbers
edited body; edited tags
Oct
25
asked Relatively tight upper and lower bounds for surreal numbers
Oct
25
revised How many times will the statement 5 be executed?
added 32 characters in body; edited title
Oct
25
revised A limit problem with sine
fixed sin
Oct
24
comment Why can't you square both sides of an equation?
@Manishearth: To cite your comment: "Squaring both sides of a consistent equation will only make you gain solutions, not lose them." This implies that he (a) doesn't gain solutions (he does), and (b) he loses solutions (he doesn't).
Oct
24
comment What does $\frac{dx}{dx}=1$ mean?
@E.A.Shams: I've now updated my answer.
Oct
24
revised What does $\frac{dx}{dx}=1$ mean?
added 606 characters in body
Oct
24
comment What does $\frac{dx}{dx}=1$ mean?
@E.A.Shams: How can you change $x$ without changing $x$? Indeed, $x$ changes by exactly the value by which you change $x$, so the quotient of both changes is obviously $1$.
Oct
24
revised What does $\frac{dx}{dx}=1$ mean?
added 312 characters in body
Oct
24
answered What does $\frac{dx}{dx}=1$ mean?
Oct
24
comment Why can't you square both sides of an equation?
@Manishearth: He did gain a solution: He started from an equation with zero solutions ($\sqrt{x}=-3$) and arrived at an equation with one solution ($x=9$). Which solution do you think he lost?
Oct
24
comment Why can't you square both sides of an equation?
You don't have to invoke $f^{-1}$: The definition of "injective" is $f(a)=f(b)\implies a=b$, no intermediate step required.
Oct
19
comment If $|f(x)+g(x)|=|f(x)|+|g(x)|$ and $|f(x)|=\lambda |g(x)|$ do we have $f(x)=\lambda g(x)$?
The first condition is definitely< not sufficient, as it is fulfilled for every pair of non-negative functions, even if they are not constant multiples of each other, say $e^x$ and $e^{2x}$. Note that the absolute value is not a norm on the space of functions; rather it maps functions to other functions.
Oct
19
comment Inequality of complex numbers
Hint: What is $(1-\left|z\right|)(1-\left|w\right|)$?
Oct
19
comment How to solve $ xyy'' − 2x(y')^2 + yy' = 0$
I would divide by $y^2$, and then notice that it can be rewritten in terms of $y'/y$ and its derivative.