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is bounded linear operator necessarily continuous?
Let $U, V$ be separable Banach spaces. Suppose we have a bounded, linear operator $C : U\to V$. Questions are the following *) Shall $C$ be continuous sin...
Apr 22, 2026
Archive: News
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I need help finding a tangent line to a parabola.
This is the question. A parabola $y=ax^2 + bx + x$ has vertex $A(2,1)$ and passes through $B(1,0)$. Find the equation of lines passing through $(0,4)$ tha...
Apr 22, 2026
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how to justify the logistic function is the inverse of the natural logit function?
per wiki The logistic function is the inverse of the natural logit function The standard logistic function looks like (equation_1) $$ {\displaystyle {\beg...
Apr 22, 2026
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T/F: any number that can be written as a fraction is rational.
Any number that can be written as a fraction is rational. I am being asked this question, and I believe it is true but for some reason,I feel that there i...
Apr 22, 2026
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Maths brain teaser. Fifty minutes ago it was four times as many minutes past three o'clock
Fifty minutes ago it was four times as many minutes past three o'clock. How many minutes is it to six o'clock..? I have got the solution online ...
Apr 22, 2026
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How to define the complex square root $ \sqrt{z} $?
We need to define the complex square root $ \sqrt{z} $ on a small open $ U \subset \mathbb{C} $, for example a disc. Let put : $ \mathcal{F} (U) = \{\ f: ...
Apr 22, 2026
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How to Solve 3x+9 is congruent to 8 mod 11?
I need five solutions to the above problem, but I'm not sure where to start with this.
Apr 22, 2026
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Quick way to solve $yy''-(y')^2=y^4$.
This is a simple yet ugly ODE (arising from Euler-Lagrange equations): $$yy''-(y')^2=y^4$$ What method could I use to quickly solve it? I b...
Apr 22, 2026
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Why do we need an integral to prove that $\frac{22}{7} > \pi$?
We know this famous (and beautiful) integral which shows that $\dfrac{22}{7} > \pi$ as : $$0 < \int_0^1 \frac{x^4(1-x)^4}{1+x^2} \, dx = \frac{22}{7...
Apr 22, 2026
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Self-studying multivariable real analysis (integration)?
As the title says, I would like to self-study multivariable real analysis (integration) and I need some recommendations (resources, books, videos, ...). I...
Apr 22, 2026
