TEDSF Q&A - Recent questions and answers in College Questions
https://tedsf.org/qna/qa/academic-questions/college-questions
Powered by Question2AnswerDoes every Boolean algebra has an ultrafilter on it?
https://tedsf.org/qna/2040/does-every-boolean-algebra-has-an-ultrafilter-on-it
Does every Boolean algebra has an ultrafilter on it?College Questionshttps://tedsf.org/qna/2040/does-every-boolean-algebra-has-an-ultrafilter-on-itSat, 10 Aug 2019 19:41:32 +0000What is the Baire Category Theorem?
https://tedsf.org/qna/2039/what-is-the-baire-category-theorem
What is the Baire Category Theorem?College Questionshttps://tedsf.org/qna/2039/what-is-the-baire-category-theoremSat, 10 Aug 2019 19:40:42 +0000What is the Loewenheim-Skolem Theorem?
https://tedsf.org/qna/2038/what-is-the-loewenheim-skolem-theorem
What is the Loewenheim-Skolem Theorem?College Questionshttps://tedsf.org/qna/2038/what-is-the-loewenheim-skolem-theoremSat, 10 Aug 2019 19:39:59 +0000Does every infinite set has a denumerable subset?
https://tedsf.org/qna/2037/does-every-infinite-set-has-a-denumerable-subset
Does every infinite set has a denumerable subset?College Questionshttps://tedsf.org/qna/2037/does-every-infinite-set-has-a-denumerable-subsetSat, 10 Aug 2019 19:38:09 +0000Is the union of countably many countable sets is countable?
https://tedsf.org/qna/2036/is-the-union-of-countably-many-countable-sets-is-countable
Is the union of countably many countable sets is countable?College Questionshttps://tedsf.org/qna/2036/is-the-union-of-countably-many-countable-sets-is-countableSat, 10 Aug 2019 19:37:25 +0000What is Zorn's Lemma?
https://tedsf.org/qna/2035/what-is-zorns-lemma
What is Zorn's Lemma?College Questionshttps://tedsf.org/qna/2035/what-is-zorns-lemmaSat, 10 Aug 2019 19:36:26 +0000What is Tychonoff's Theorem?
https://tedsf.org/qna/2034/what-is-tychonoffs-theorem
What is Tychonoff's Theorem?College Questionshttps://tedsf.org/qna/2034/what-is-tychonoffs-theoremSat, 10 Aug 2019 19:35:42 +0000Is it true that, for any cardinals $k$ and $l$, either $k<l$ or $k=l$ or $k>l$?
https://tedsf.org/qna/2033/is-it-true-that-for-any-cardinals-k-and-l-either-k-l-or-k-l-or-k-l
Is it true that, for any cardinals $k$ and $l$, either $k<l$ or $k=l$ or $k>l$?College Questionshttps://tedsf.org/qna/2033/is-it-true-that-for-any-cardinals-k-and-l-either-k-l-or-k-l-or-k-lSat, 10 Aug 2019 19:34:58 +0000Does every vector space have a basis?
https://tedsf.org/qna/2032/does-every-vector-space-have-a-basis
Does every vector space have a basis?College Questionshttps://tedsf.org/qna/2032/does-every-vector-space-have-a-basisSat, 10 Aug 2019 19:34:02 +0000What is platonism in mathemetics?
https://tedsf.org/qna/2031/what-is-platonism-in-mathemetics
What is platonism in mathemetics?College Questionshttps://tedsf.org/qna/2031/what-is-platonism-in-mathemeticsSat, 10 Aug 2019 19:33:03 +0000For any set $X$ is there a function $f$, with domain $X\backslash{0}$, so that $f(x)$ is a member of $x$ for every nonempty $x$ in $X$?
https://tedsf.org/qna/2030/for-any-set-x-is-there-a-function-f-with-domain-x-backslash-0-so-that-f-x-is-a-member-of-x-for-every-nonempty-x-in-x
For any set $X$ is there a function $f$, with domain $X\backslash{0}$, so that $f(x)$ is a member of $x$ for every nonempty $x$ in $X$?College Questionshttps://tedsf.org/qna/2030/for-any-set-x-is-there-a-function-f-with-domain-x-backslash-0-so-that-f-x-is-a-member-of-x-for-every-nonempty-x-in-xSat, 10 Aug 2019 19:31:40 +0000Given any set $S$ of mutually disjoint nonempty sets, is there a set $C$ containing a single member from each element of $S$?
https://tedsf.org/qna/2029/given-any-set-s-of-mutually-disjoint-nonempty-sets-is-there-a-set-c-containing-a-single-member-from-each-element-of-s
Given any set $S$ of mutually disjoint nonempty sets, is there a set $C$ containing a single member from each element of $S$?College Questionshttps://tedsf.org/qna/2029/given-any-set-s-of-mutually-disjoint-nonempty-sets-is-there-a-set-c-containing-a-single-member-from-each-element-of-sSat, 10 Aug 2019 19:30:29 +0000Is the Cartesian product of nonempty sets is nonempty, even if the product is of an infinite family of sets?
https://tedsf.org/qna/2028/is-the-cartesian-product-of-nonempty-sets-is-nonempty-even-if-the-product-is-of-an-infinite-family-of-sets
Is the Cartesian product of nonempty sets is nonempty, even if the product is of an infinite family of sets?College Questionshttps://tedsf.org/qna/2028/is-the-cartesian-product-of-nonempty-sets-is-nonempty-even-if-the-product-is-of-an-infinite-family-of-setsSat, 10 Aug 2019 19:29:22 +0000What is an integral domain in mathematics?
https://tedsf.org/qna/2027/what-is-an-integral-domain-in-mathematics
What is an integral domain in mathematics?College Questionshttps://tedsf.org/qna/2027/what-is-an-integral-domain-in-mathematicsSat, 10 Aug 2019 19:27:55 +0000What is a monoid?
https://tedsf.org/qna/2026/what-is-a-monoid
What is a monoid?College Questionshttps://tedsf.org/qna/2026/what-is-a-monoidSat, 10 Aug 2019 19:27:04 +0000Can we count past infinity?
https://tedsf.org/qna/1299/can-we-count-past-infinity
Can we count past infinity?College Questionshttps://tedsf.org/qna/1299/can-we-count-past-infinityTue, 04 Jun 2019 03:25:04 +0000How big is infinity?
https://tedsf.org/qna/1298/how-big-is-infinity
How big is infinity?College Questionshttps://tedsf.org/qna/1298/how-big-is-infinityTue, 04 Jun 2019 03:24:31 +0000Is 1 closer to infinity than 0?
https://tedsf.org/qna/1297/is-1-closer-to-infinity-than-0
Is 1 closer to infinity than 0?College Questionshttps://tedsf.org/qna/1297/is-1-closer-to-infinity-than-0Tue, 04 Jun 2019 03:23:40 +0000Answered: What is $\aleph$ in mathematics?
https://tedsf.org/qna/1289/what-is-aleph-in-mathematics?show=1296#a1296
Aleph is a letter from the Hebrew alphabet. Georg Cantor, a deeply religious man, introduced it to denote cardinalities of sets in his effort to provide a rigorous axiomatization of set theory.<br />
<br />
Two of the results of Cantor's work appear paradoxical.<br />
<br />
The first paradox has to do with Aleph-0 - the cardinality of all countably infinite sets: Although the sets N, Z and Q are strict subsets of each other, they all have the same cardinality i.e. Aleph-0.<br />
<br />
The second paradox has to do with Aleph-1 - the cardinality of R (or just the interval [0, 1]), which is equal to the cardinality of the set of all subsets of Z i.e. 2 to the power Aleph-0.<br />
<br />
It appears that the continuum hypothesis (CH - Hilbert 1st Problem) that speculates on the existence of an infinite between Aleph-0 and Aleph-1, is quite independent of Axioms chosen for Axiomatisation of Set theory (e.g. Zermelo-Frankel + Axiom of choice). CH is thus an example of Godel Incompleteness Theorem: A statement that is neither provable nor disprovable.College Questionshttps://tedsf.org/qna/1289/what-is-aleph-in-mathematics?show=1296#a1296Mon, 03 Jun 2019 11:05:11 +0000Who can interpret Euler's identity $e^{i \pi} + 1 = 0$?
https://tedsf.org/qna/1293/who-can-interpret-eulers-identity-e-i-pi-1-0
Who can interpret **Euler's identity** $e^{i \pi} + 1 = 0 $?College Questionshttps://tedsf.org/qna/1293/who-can-interpret-eulers-identity-e-i-pi-1-0Mon, 03 Jun 2019 04:32:11 +0000Where does the Cauchy-Schwarz inequality apply in life?
https://tedsf.org/qna/1291/where-does-the-cauchy-schwarz-inequality-apply-in-life
Where does the Cauchy-Schwarz inequality apply in life? \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \] where $a_k$ and $b_k$ are real numbers, for any $k$College Questionshttps://tedsf.org/qna/1291/where-does-the-cauchy-schwarz-inequality-apply-in-lifeMon, 03 Jun 2019 03:45:58 +0000Is $0.\overline{3} = \frac{1}{3}$ a true statement?
https://tedsf.org/qna/1288/is-0-overline-3-frac-1-3-a-true-statement
Is $0.\overline{3} = \frac{1}{3}$ a true statement?College Questionshttps://tedsf.org/qna/1288/is-0-overline-3-frac-1-3-a-true-statementMon, 03 Jun 2019 02:01:58 +0000Why do mathematicians like using the signs $\lambda,\xi,\pi,\theta, \mu,\Phi,\Omega,\Delta$
https://tedsf.org/qna/1287/why-do-mathematicians-like-using-the-signs-lambda-xi-pi-theta-mu-phi-omega-delta
Why do mathematicians like using the signs $\lambda,\xi,\pi,\theta, \mu,\Phi,\Omega,\Delta$College Questionshttps://tedsf.org/qna/1287/why-do-mathematicians-like-using-the-signs-lambda-xi-pi-theta-mu-phi-omega-deltaMon, 03 Jun 2019 02:00:55 +0000What does the statement $\forall x \in \mathbf{R}: \qquad x^{2} \geq 0$ mean?
https://tedsf.org/qna/1286/what-does-the-statement-forall-x-in-mathbf-r-qquad-x-2-geq-0-mean
What does the statement $\forall x \in \mathbf{R}: \qquad x^{2} \geq 0$ mean?real number math translationCollege Questionshttps://tedsf.org/qna/1286/what-does-the-statement-forall-x-in-mathbf-r-qquad-x-2-geq-0-meanMon, 03 Jun 2019 01:59:30 +0000Is it true that $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}$ ?
https://tedsf.org/qna/1285/is-it-true-that-lim-n-to-infty-sum-k-1-n-frac-1-k-2-frac-pi-2-6
Is it true that $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}$ ?College Questionshttps://tedsf.org/qna/1285/is-it-true-that-lim-n-to-infty-sum-k-1-n-frac-1-k-2-frac-pi-2-6Mon, 03 Jun 2019 01:57:51 +0000How do you measure the Distance to the Stars?
https://tedsf.org/qna/1263/how-do-you-measure-the-distance-to-the-stars
How do you measure the Distance to the Stars?College Questionshttps://tedsf.org/qna/1263/how-do-you-measure-the-distance-to-the-starsMon, 27 May 2019 08:40:45 +0000A farmer has 40m of fencing. What is the maximum area he can enclose?
https://tedsf.org/qna/1262/a-farmer-has-40m-of-fencing-what-is-the-maximum-area-he-can-enclose
A farmer has 40m of fencing. What is the maximum area he can enclose?College Questionshttps://tedsf.org/qna/1262/a-farmer-has-40m-of-fencing-what-is-the-maximum-area-he-can-encloseMon, 27 May 2019 08:39:10 +0000How is Benford's Law used to catch criminal fraudsters?
https://tedsf.org/qna/1261/how-is-benfords-law-used-to-catch-criminal-fraudsters
How is Benford's Law used to catch criminal fraudsters?College Questionshttps://tedsf.org/qna/1261/how-is-benfords-law-used-to-catch-criminal-fraudstersMon, 27 May 2019 08:37:48 +0000How much younger will I be than my twin?
https://tedsf.org/qna/1260/how-much-younger-will-i-be-than-my-twin
I built a spacecraft capable of traveling at 95% the speed of light. I said goodbye to my twin sister and hopped aboard, flew for a while before returning to Earth. If I experienced 10 years on the space craft, how much younger will I be than my twin?College Questionshttps://tedsf.org/qna/1260/how-much-younger-will-i-be-than-my-twinMon, 27 May 2019 08:36:25 +0000How far does this craft travel in 1 hour? What would the time dilation be for someone onboard since 1977?
https://tedsf.org/qna/1259/how-far-does-this-craft-travel-in-1-hour-what-would-the-time-dilation-be-for-someone-onboard-since-1977
Voyager 1, launched in 1977 and now currently about 1.8×10^10 km away from Earth is traveling at around 17km/s. How far does this craft travel in 1 hour? What would the time dilation be for someone onboard since 1977?College Questionshttps://tedsf.org/qna/1259/how-far-does-this-craft-travel-in-1-hour-what-would-the-time-dilation-be-for-someone-onboard-since-1977Mon, 27 May 2019 08:35:29 +0000How much longer will he live (from a stationary viewpoint) compared to if he had been a bus driver?
https://tedsf.org/qna/1258/how-much-longer-will-he-live-from-a-stationary-viewpoint-compared-to-if-he-had-been-a-bus-driver
A long working air steward spends a cumulative total of 5 years in the air – flying at an average speed of 900km/h. How much longer will he live (from a stationary viewpoint) compared to if he had been a bus driver?College Questionshttps://tedsf.org/qna/1258/how-much-longer-will-he-live-from-a-stationary-viewpoint-compared-to-if-he-had-been-a-bus-driverMon, 27 May 2019 08:34:32 +0000Why do engineers think that Fourier Transforms is the most important tool in mathematics?
https://tedsf.org/qna/1257/why-do-engineers-think-that-fourier-transforms-is-the-most-important-tool-in-mathematics
<p>Why do engineers think that Fourier Transforms is the most important tool in mathematics?</p>
<p><img alt="Why do engineers think that Fourier Transforms is the most important tool in mathematics?" src="https://mathsgee.com/qna/?qa=blob&qa_blobid=4904253059624814639" style="height:400px; width:600px"></p>College Questionshttps://tedsf.org/qna/1257/why-do-engineers-think-that-fourier-transforms-is-the-most-important-tool-in-mathematicsMon, 27 May 2019 08:27:11 +0000Does Zeno's paradox make sense?
https://tedsf.org/qna/1256/does-zenos-paradox-make-sense
Does Zeno's paradox make sense?College Questionshttps://tedsf.org/qna/1256/does-zenos-paradox-make-senseMon, 27 May 2019 08:24:26 +0000Is Intergalactic space travel possible?
https://tedsf.org/qna/1255/is-intergalactic-space-travel-possible
Is Intergalactic space travel possible?College Questionshttps://tedsf.org/qna/1255/is-intergalactic-space-travel-possibleMon, 27 May 2019 08:23:33 +0000Why is the Gini Coefficient the best way of measuring inequality?
https://tedsf.org/qna/1254/why-is-the-gini-coefficient-the-best-way-of-measuring-inequality
Why is the Gini Coefficient the best way of measuring inequality?College Questionshttps://tedsf.org/qna/1254/why-is-the-gini-coefficient-the-best-way-of-measuring-inequalityMon, 27 May 2019 08:22:31 +0000Why are people saying quantum mechanics is the best thing to happen in maths and science ever?
https://tedsf.org/qna/1253/why-are-people-saying-quantum-mechanics-is-the-best-thing-to-happen-in-maths-and-science-ever
Why are people saying quantum mechanics is the best thing to happen in maths and science ever?College Questionshttps://tedsf.org/qna/1253/why-are-people-saying-quantum-mechanics-is-the-best-thing-to-happen-in-maths-and-science-everMon, 27 May 2019 08:21:12 +0000What is projective geometry?
https://tedsf.org/qna/1252/what-is-projective-geometry
What is projective geometry?College Questionshttps://tedsf.org/qna/1252/what-is-projective-geometryMon, 27 May 2019 08:20:09 +0000How can one optimize the volume of a given cuboid?
https://tedsf.org/qna/1251/how-can-one-optimize-the-volume-of-a-given-cuboid
How can one optimize the volume of a given cuboid?College Questionshttps://tedsf.org/qna/1251/how-can-one-optimize-the-volume-of-a-given-cuboidMon, 27 May 2019 08:19:30 +0000Is the number 277777788888899 special in mathematics?
https://tedsf.org/qna/1250/is-the-number-277777788888899-special-in-mathematics
Is the number 277777788888899 special in mathematics?College Questionshttps://tedsf.org/qna/1250/is-the-number-277777788888899-special-in-mathematicsMon, 27 May 2019 08:18:24 +0000Can the Mandelbrot Set be plotted manually?
https://tedsf.org/qna/1249/can-the-mandelbrot-set-be-plotted-manually
Can the Mandelbrot Set be plotted manually?College Questionshttps://tedsf.org/qna/1249/can-the-mandelbrot-set-be-plotted-manuallyMon, 27 May 2019 08:17:34 +0000Which base shape ensures that a pyramid is most stable?
https://tedsf.org/qna/1248/which-base-shape-ensures-that-a-pyramid-is-most-stable
Which base shape ensures that a pyramid is most stable?College Questionshttps://tedsf.org/qna/1248/which-base-shape-ensures-that-a-pyramid-is-most-stableMon, 27 May 2019 08:16:18 +0000Show that there exists an infinite family of involutes for a gives curve
https://tedsf.org/qna/917/show-that-there-exists-an-infinite-family-of-involutes-for-a-gives-curve
Show that there exists an infinite family of involutes for a gives curveCollege Questionshttps://tedsf.org/qna/917/show-that-there-exists-an-infinite-family-of-involutes-for-a-gives-curveSun, 19 May 2019 02:52:03 +0000If $x = [x_0,x_1,x_2]^T$ and $z = [z_0,z_1,z_2]^T$ are column vectors, then evaluate:
https://tedsf.org/qna/912/if-x-x0-x1-x2-t-and-z-z0-z1-z2-t-are-column-vectors-then-evaluate
<p>If $x = [x_0,x_1,x_2]^T$ and $z = [z_0,z_1,z_2]^T$ are column vectors, then evaluate:</p>
<ol>
<li>$x^T \cdot z$ (dot product)</li>
<li>$x \cdot z^T$ (matrix product)</li>
<li>$x \times z$ (cross product)</li>
</ol>College Questionshttps://tedsf.org/qna/912/if-x-x0-x1-x2-t-and-z-z0-z1-z2-t-are-column-vectors-then-evaluateSun, 19 May 2019 02:45:57 +0000What is the translation into English of $\forall x[E(x) \lor O(x)]$ ?
https://tedsf.org/qna/907/what-is-the-translation-into-english-of-forall-x-e-x-lor-o-x
What is the translation into English of $\forall x[E(x) \lor O(x)]$ ?College Questionshttps://tedsf.org/qna/907/what-is-the-translation-into-english-of-forall-x-e-x-lor-o-xSun, 19 May 2019 02:33:14 +0000What if the axioms of mathematics are actually wrong?
https://tedsf.org/qna/824/what-if-the-axioms-of-mathematics-are-actually-wrong
What if the axioms of mathematics are actually wrong?College Questionshttps://tedsf.org/qna/824/what-if-the-axioms-of-mathematics-are-actually-wrongSat, 27 Apr 2019 22:59:25 +0000When is division by zero ever defined in mathematics?
https://tedsf.org/qna/667/when-is-division-by-zero-ever-defined-in-mathematics
When is division by zero ever defined in mathematics? College Questionshttps://tedsf.org/qna/667/when-is-division-by-zero-ever-defined-in-mathematicsSat, 23 Mar 2019 01:12:55 +0000For what real values of $x$ is:
https://tedsf.org/qna/661/for-what-real-values-of-x-is
For what real values of $x$ is:<br />
<br />
$$\sqrt{(x + \sqrt{2x -1})} + \sqrt{(x - \sqrt{2x -1})} $$College Questionshttps://tedsf.org/qna/661/for-what-real-values-of-x-isSat, 16 Mar 2019 06:00:17 +0000