Difference between "≈", "≃", and "≅" - Mathematics Stack Exchange
In LaTeX it is coded as \cong. ∼ ∼ is a similarity in geometry and can be used to show that two things are asymptotically equal (they become more equal as you increase a variable like n n). This is a weaker statement than the other two. In LaTeX it is …
Proving that the set of limit points of a set is closed
20. Let ˆS be the set of all limit points of S. Prove that ˆS is a closed set. Proof: Suppose x0 is a limit point of ˆS. Then given ε> 0 there exists x ∈ ˆS with |x − x0 | <ε 2. Now x ∈ ˆS is a limit point of S so there exists x ′ ∈ S such that |x ′ − x | <ε 2. Now |x ′ − x0 | = | x ′ − x + x − x0 | ≤ | x ...
how to convert 1e+11 into number? - Mathematics Stack Exchange
Jan 14, 2017 · 1 e+11 = 1 ×10+11 1 e+11 = 1 × 10 + 11. You should know that 10 10 raised to any positive integer is a 1 1 with that many 0 0 s behind it. So. 10+11 = 100000000000 10 + 11 = 100000000000. thank you for your reply. i might be able to accept your answer after 11mins (from now) as shown in SO msg.
Two cards are drawn without replacement from an ordinary deck …
Oct 8, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
trigonometry - when to use sine vs cosine vs tangent
There are relationships between the different trig functions, e.g. sin d = 1 −cos2 d− −−−−−−−√ sin d = 1 − cos 2 d. However it's a lot easier to find them directly given a standard right-angled triangle problem. For reference, the identities that you can use are: sin2 x +cos2 x tan2 x + 1 1 +cot2 x = 1 =sec2 x, where sec x ...
Area of intersection between two circles - Mathematics Stack …
So, the area of one half of the intersection is the area of a circular segment with angle θ = 2π 3 and radius r, which gives an area of r2 2(θ − sinθ) = r2 2 (2π 3 − √3 2) and so the area of the entire intersection is twice this. This gives an area of r2(2π 3 − √3 2). @MhenniBenghorbal I'm a little confused by the edit.
What's an intuitive way to think about the determinant?
In my linear algebra class, we just talked about determinants. So far I’ve been understanding the material okay, but now I’m very confused. I get that when the determinant is zero, the matrix doesn’t have an inverse. I can find the determinant of a $2\times 2$ matrix by the formula.
Is arrow notation for vectors "not mathematically mature"?
Jan 7, 2015 · Therefore, there's a critical period where you will get very confused if you don't carefully distinguish between them. Consistently writing vectors and scalars differently will likely help with this. However, once you understand the difference and have become accustomed to distinguishing them in your mind, it's less useful to write them very ...
Proving sequence convergence - Mathematics Stack Exchange
Oct 28, 2014 · Using only the definition 4.1.2 prove the following: "Definition 4.1.2 A sequence (sn) is said to converge to the real number s provided that for every ε> 0 there exists a natural number N such that for all n ∈ N, n ≥ N implies that | sn − s | <ε. If (sn) converges to s, then s is called the limit of the sequence (sn) and we write limn ...
Expected value of the number of flips until the first head
Jun 12, 2020 · I'm really confused, and if someone were to provide an answer, I would really appreciate it if they could go into detail. $\endgroup$ – hyperdo Commented Mar 19, 2015 at 3:09