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Jul
2
comment Given a Line Parametrization, Finding another Equation
@rebecca: Rather, when $t=0,$ you obtain the point $(1,1,1).$
Jul
2
revised In a commutative ring without identity, is $(a)(b)\subset (ab)$ or $(ab)\subset (a)(b)$?
added 14 characters in body
Jul
2
comment Given a Line Parametrization, Finding another Equation
@rebecca: Have you found two other points on the plane, yet? If not, you should do so. If so, what are they?
Jul
2
comment Prove that $f(x) = x$ has a solution on [0,1]
Put another way, every continuous function on $[0,1]$ has at least one fixed point.
Jul
2
comment Prove that $f(x) = x$ has a solution on [0,1]
The problem isn't defining the function to be $f(x)=x.$ It's saying that if $f$ is any continuous function $[0,1]\to[0,1],$ then there is some $x\in[0,1]$ such that $f(x)=x.$
Jul
1
revised Finding the Characteristic Equation
added 375 characters in body
Jul
1
answered Finding the Characteristic Equation
Jul
1
comment Defining exponentiation on the integers
+1: Nicely done.
Jul
1
comment Defining exponentiation on the integers
Also, this doesn't address how to deal with nonnatural exponents.
Jul
1
comment Defining exponentiation on the integers
Did you forget the binomial coefficients, there?
Jun
30
comment Show that $f$ is bounded.
Also, how did you decide that $g(a)<0$ and $g(b)>0$? There's no reason to suspect that's true.
Jun
30
comment Show that $f$ is bounded.
Are you sure you aren't supposed to use the Extreme Value Theorem?
Jun
28
comment If a function is left- and right-differentiable everywhere, how much can the one-sided derivatives disagree?
+1: Excellent! Many thanks, David.
Jun
28
accepted If a function is left- and right-differentiable everywhere, how much can the one-sided derivatives disagree?
Jun
28
revised Let $f(x,y)=(x^2)/(x^2+y^2)$, show that the domain for this function is all points $(x,y)$ except $(0,0)$
added 80 characters in body
Jun
28
answered Let $f(x,y)=(x^2)/(x^2+y^2)$, show that the domain for this function is all points $(x,y)$ except $(0,0)$
Jun
28
comment Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
@Learner: I imagine that zhw considered first what functions send exactly the real and imaginary lines to the real line. One such function is $z\mapsto z^2.$ Hence $z\mapsto iz^2$ maps exactly the real and imaginary lines to the imaginary line, whence composition with $w\mapsto e^w$ yields the desired result. A similar approach is to consider $\sin(z^2)$.
Jun
28
asked If a function is left- and right-differentiable everywhere, how much can the one-sided derivatives disagree?
Jun
26
answered Determine whether the following argument is valid
Jun
26
comment $A=\{A,\emptyset\}$ and axiom of regularity
Now that you've edited your answer, I see that you've caught on to the key point. ^_^ Your original phrasing seemed to have both "senses" saying precisely the same thing (albeit in different words).