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| age | ||
| visits | member for | 2 years, 5 months |
| seen | 5 hours ago | |
| stats | profile views | 842 |
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14h |
revised |
Prove $\ln{(\frac {x}{y})} = \ln{x} - \ln{y}$ using the definition $\int_1^x\frac{1}{t}dt = \ln{x}$. fixed the title |
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1d |
accepted | Strong characterization of $\mathbb C$ with respect to $\mathbb R$ |
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1d |
comment |
Strong characterization of $\mathbb C$ with respect to $\mathbb R$ @user1 : Edited to clarify more, hope this helps in making what I am trying to say clearer. |
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1d |
revised |
Strong characterization of $\mathbb C$ with respect to $\mathbb R$ added 248 characters in body |
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1d |
comment |
Strong characterization of $\mathbb C$ with respect to $\mathbb R$ I know $\mathbb R^2$ is not a field, but 2 tuple arithmetic rules like (a,b)(c,d)=(ac-db,ad+bc) etc. coupled with $\mathbb R^2$ make a field, but are there rules other than (a,b)(c,d)=(ac-db,ad+bc) combined with $\mathbb R^2$ that make a field? |
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1d |
comment |
Strong characterization of $\mathbb C$ with respect to $\mathbb R$ @user1 : if you have seen the 2 tuple approach to complex numbers, where there is no mention of $i$ but instead (0,1), or the matrix form is used, then it seemed natural to think as (0,1) as a point in $\mathbb R^2$ with some funny rules for addition (a,b)+(b,c)=(a+b,c+d) and multiplication (a,b)(b,c)=(ab-bc,ac+bd) , {(a,b),(c,d)} being points in $\mathbb R^2$ with strange arithmetic, where R just becomes (a,0),(b,0), etc. |
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1d |
asked | Strong characterization of $\mathbb C$ with respect to $\mathbb R$ |
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1d |
revised |
How to solve this integral for a hyperbolic bowl? Since this became community wiki, non one needs to take responsibility of a mistake |
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1d |
revised |
Simplify $\sqrt n+\frac {1}{\sqrt n}$ for $n=7+4\sqrt3$ edited tags; edited title |
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2d |
revised |
Zero to the zero power - Is $0^0=1$? misleading title, 0^0 is NOT 1. |
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2d |
comment |
Test of convergence of $\int_{-\infty}^{\infty} \dfrac{x^6+6}{x^8+8}dx$ @Siddhant Trivedi : Why change from $g(x) = \frac{1}{x^2}$ to $g(x) = 1/x^2$ ? |
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2d |
revised |
Test of convergence of $\int_{-\infty}^{\infty} \dfrac{x^6+6}{x^8+8}dx$ edited title |
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2d |
reviewed | Approve suggested edit on Test of convergence of $\int_{-\infty}^{\infty} \dfrac{x^6+6}{x^8+8}dx$ |
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2d |
answered | $\frac{d}{dx}\int_{0}^{e^{x^{2}}} \frac{1}{\sqrt{t}}dt$ |
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2d |
revised |
$\frac{d}{dx}\int_{0}^{e^{x^{2}}} \frac{1}{\sqrt{t}}dt$ edited title |
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2d |
revised |
Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $ edited title |
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2d |
revised |
$\sum^n_{j=0} (-1)^{j-1}j $ edited title |
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2d |
revised |
$\int_0^{\pi/4}\!\frac{\mathrm dx}{2+\sin x}$ , $\int_0^{2\pi}\!\frac{\mathrm dx}{2+\sin x}$ edited title |
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May 14 |
revised |
$\int^1_0 \frac{xdx}{x^2+2x+1}$ edited title |
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May 14 |
revised |
$\int_0^\pi\frac{3\cos x+\sqrt{8+\cos^2 x}}{\sin x}x\ \mathrm dx$ edited title |
