Top new questions this week: |
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Why can't a set have two elements of the same value?Suppose I have two sets, $A$ and $B$: $$A = \{1, 2, 3, 4, 5\} \\ B = \{1, 1, 2, 3, 4\}$$ Set $A$ is valid, but set $B$ isn't because not all of its elements are unique. My question is, why can't …
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In primary school I was showed this. Why does it work?When I was in primary school a teacher showed us the following exercise in arithmetic. Take any 3 digit number between 201 and 998 provided that the hundreds digit is bigger than the ones digit and …
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There is no smallest infinity in calculus?Somewhat of a basic question, but I tried mixing set theory and calculus and the result is a giant mess. From set theory (assume ZFC) we know there is a smallest infinite cardinal, $\aleph_0$, and …
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Why are huge binary numbers about 3.3218 times longer than their decimal counterpart?Why are huge binary nubers about $3.3218$ times longer than their decimal counterpart? I thought about this when I was writing this Python code: huge_number = 21**31**3 # ** is the power operator …
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Baffled by resolving number listMy son's Maths homework was to do with number patterns/sequences. "What is the nth term?". He'd done very well, but the last sequence was something like this: 19,77,265,715,1607,3169 He was adamant …
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1/1000 chance of a reaction. If you do the action 1000 times, whats the new chance the reaction occurs?A hypothetical example: You have a 1/1000 chance of being hit by a bus when crossing the street. However, if you perform the action of crossing the street 1000 times, then your chance of being …
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Closed form for ${\large\int}_0^1\frac{\ln^3x}{\sqrt{x^2-x+1}}dx$This is a follow-up to my earlier question Closed form for ${\large\int}_0^1\frac{\ln^2x}{\sqrt{1-x+x^2}}dx$. Is there a closed form for this integral? …
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Greatest hits from previous weeks: |
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'Obvious' theorems that are actually falseIt's one of my real analysis professor's favourite sayings that "being obvious does not imply that it's true". Now, I know a fair few examples of things that are obviously true and that can be proved …
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Mathematicians ahead of their time?In every field there's always that person who's just years ahead of their time. For instance, Paul Morphy (born 1837) is said to have retired from chess because he found no one to match his technique …
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Can you answer these? |
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$\sin$ vs. $sin$ - history and usageOne thing newcomers to TeX or MathJax often get wrong is that they write something like $sin(x)$ instead of $\sin(x)$ - the point being that common mathematical functions with names consisting of …
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When two projections in a C*-algebra are "almost" Murray-von Neumann equivalent, they are equivalentLet $A$ be a C*-algebra and $p,q \in A$ be projections. Assume there is an element $a\in A$ such that $\|aa^*-p\|<\frac{1}{4}$ and $\|a^*a-q\|<\frac{1}{4}$. Then there is a partial isometry $v$ …
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On distributivity of lattice of group topologiesLet $\frak L$ be the set of all topologies $\mathcal T$ on $\Bbb Q$ (the additive group of all rational numbers) such that $(\Bbb Q,\mathcal T)$ is a topological group. Then $(\frak L,\subseteq)$ is a …
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