id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
4,286
|
n \cdot m_1 + n \cdot m_2 = m_1 \cdot n + m_2 \cdot n
|
-12,025
|
\frac{1}{60}\cdot 59 = s/(8\cdot \pi)\cdot 8\cdot \pi = s
|
30,240
|
1^2 + 2^2 + 3^2 + 4^2 = (1 + 2 + 3 + 4) \cdot 3
|
9,249
|
\cos(d) = \cos(d + 2\pi)
|
12,509
|
1 - z + \frac{z^2}{2} - \ldots = e^{-z}
|
-2,814
|
10 \cdot \sqrt{13} = \sqrt{13} \cdot (5 + 1 + 4)
|
27,690
|
\cos(2 \cdot x) = \frac{1}{1 + \tan^2(x)} \cdot (-\tan^2(x) + 1)
|
-8,497
|
8 = -\frac{32}{-4}
|
657
|
A \cap A \cap V^\complement = A \cap (A^\complement \cup V^\complement) = A \cap V^\complement
|
-18,695
|
0.8833 = 0.9192 - 0.0359
|
26,898
|
25 \cdot x^2 + 13 = (\frac{13}{25} + x^2) \cdot 25
|
31,023
|
314 = 49 \cdot (-1) + 11^2 \cdot 3
|
1,394
|
x^l\cdot x^0 = x^{l + 0} = x^l
|
13,019
|
(-1) + z^2 = (z + (-1)) \cdot \left(z + 1\right)
|
-21,934
|
\dfrac{5}{6} + \dfrac{3}{5} = {\dfrac{5 \times 5}{6 \times 5}} + {\dfrac{3 \times 6}{5 \times 6}} = {\dfrac{25}{30}} + {\dfrac{18}{30}} = \dfrac{{25} + {18}}{30} = \dfrac{43}{30}
|
27,055
|
(499 \cdot (-1) + 503) \cdot 509 = 2036
|
29,992
|
(a+1)^2-a^2=a^2+2a+1-a^2=2a+1
|
-10,043
|
-\frac{1}{8}*4 = -\frac{1}{2}
|
40,862
|
0 = \frac{0}{0}\cdot 0
|
28,264
|
2(-1) + 2x = (x + (-1))*2
|
-12,380
|
\sqrt{120} = \sqrt{30} \cdot 2
|
-12,358
|
44 = 2^2*11
|
23,065
|
\sqrt{25*k + 49} = 5*\sqrt{k + 2 - 1/25} \approx 5*\sqrt{k + 2}
|
17,454
|
\binom{n + (-1)}{k + \left(-1\right)} = \frac{\binom{n}{k}}{n} \cdot k
|
-15,321
|
\frac{1}{(\frac1np^5) \cdot (\frac1np^5) n^2} = \frac{1}{n^2 \dfrac{p^{10}}{n^2}}
|
29,920
|
s_k \cdot s_x = s_k \cdot s_x
|
-17,817
|
4 \left(-1\right) + 27 = 23
|
-369
|
\frac{1}{(9 + 3\cdot (-1))!\cdot 3!}\cdot 9! = \binom{9}{3}
|
-11,695
|
25^{-\frac{1}{2}} = \left(\frac{1}{25}\right)^{\frac12} = 1/5
|
12,021
|
\sin{2z} + 1 = t^2 \Rightarrow (-1) + t^2 = \sin{z*2}
|
-2,277
|
6/14 - \dfrac{3}{14} = \frac{1}{14}*3
|
11,898
|
(1 + x)^{n + 1} = (1 + x)^n\cdot \left(1 + x\right) \gt \left(1 + x^n\right) \left(1 + x\right) = 1 + x + x^n + x^{n + 1} \gt 1 + x^{n + 1}
|
-1,287
|
\tfrac{8*\frac{1}{3}}{\tfrac{1}{2}*(-7)} = 8/3*\left(-2/7\right)
|
-3,887
|
\dfrac{121}{44} \frac{z^5}{z^4} = \frac{121 z^5}{z^4 \cdot 44}
|
8,150
|
(I - xi^Q) (I - xi^Q) = I - xi^Q - xi^Q + xi^Q xi^Q = I - xi^Q - xi^Q
|
-29,347
|
(a - d) \left(d + a\right) = -d^2 + a^2
|
8,012
|
2y^2 = 2(y^4 + y^2) - y^4 \cdot 2
|
29,128
|
9\cdot 2\cdot 2 = 6^2
|
5,528
|
2\times n\times n\times n = n^3\times 2
|
45,987
|
1 = (\left(-1\right) \cdot \left(-1\right))^{\frac{1}{3}}
|
8,408
|
(-1) + \cos^2\left(x\right) \cdot 2 = \cos(2 \cdot x)
|
-16,672
|
6 = 6*3*x + 6*\left(-8\right) = 18*x - 48 = 18*x + 48*(-1)
|
23,054
|
\frac{\mathrm{d}}{\mathrm{d}x} x^2 \cdot x = 3x^2
|
47,463
|
0 = 1^3 + (-1)
|
30,369
|
247 = 265 + 18*\left(-1\right)
|
-7,740
|
\frac{1}{-4} (-i*8 + 12) = -\dfrac{i*8}{-4} + 12/(-4)
|
-585
|
e^{\tfrac{5}{12}\cdot \pi\cdot i\cdot 14} = (e^{5\cdot i\cdot \pi/12})^{14}
|
14,716
|
s^{r \cdot u} = \tfrac{r \cdot s \cdot u}{r \cdot u} \cdot 1 = 1/r \cdot s \cdot r \cdot u/u = s^r \cdot u/u = (s^r)^u
|
12,008
|
y^{24} + 1 = (y^{16} - y^8 + 1) \cdot (y^8 + 1)
|
-1,140
|
-1/9 \cdot 4/3 = \frac{\left(-1\right) \cdot 1/9}{1/4 \cdot 3}
|
22,370
|
z_2^{z_1 + 1} = z_2^{z_1} \cdot z_2
|
222
|
0 = 4\left(-1\right) + 3a \implies a = 4/3
|
11,731
|
z^{n + 1} = z\cdot z^n < z^n
|
19,353
|
Q\Sigma^{1/2} = Q\Sigma^{\frac12}
|
-545
|
\pi = -10\cdot \pi + \pi\cdot 11
|
24,083
|
p \cdot p + q^2 = (p + q)^2 - 2\cdot q\cdot p
|
34,364
|
0 \gt 1 + z \Rightarrow -1 \gt z
|
14,127
|
\gamma + d = \gamma + d
|
-201
|
\frac{1}{(5 + 3\cdot (-1))!\cdot 3!}\cdot 5! = \binom{5}{3}
|
2,685
|
n \cdot (x_1 + x_2) = n \cdot x_2 + n \cdot x_1
|
10,694
|
y \cdot y = y \cdot y + (-1) + 1 = (y + 1) (y + (-1)) + 1
|
33,239
|
0 = 1/z - \frac{1}{z^2} \cdot \left(X - z\right) \Rightarrow 2 \cdot z = X
|
-15,639
|
\dfrac{{q^{-20}}}{{q^{-1}p^{-3}}} = \dfrac{{q^{-20}}}{{q^{-1}}} \cdot \dfrac{{1}}{{p^{-3}}} = q^{{-20} - {(-1)}} \cdot p^{- {(-3)}} = q^{-19}p^{3}
|
23,908
|
\sinh^2{x} = (e^x - e^{-x})^2/4 = \frac14 (e^{2 x} + e^{-2 x} - 2 e^0)
|
38,034
|
34^2 = 1 + 15\cdot 77
|
17,449
|
\left(1 \leq 0 \Rightarrow 0 = 1\wedge 2 \leq 0\right) \Rightarrow 2 = 0\wedge \cdots
|
-3,102
|
\sqrt{9} \sqrt{5} + \sqrt{25} \sqrt{5} = 5\sqrt{5} + \sqrt{5}\cdot 3
|
17,003
|
\cos{2\times a} = \cos^2{a} - \sin^2{a} = 2\times \cos^2{a} + (-1)
|
16,058
|
x = \|x\| \dfrac{x}{\|x\|}
|
37,536
|
\frac{1}{0.0025^{\dfrac{1}{2}}} \cdot 0.001 = 0.02
|
12,301
|
\frac{\sqrt{2}}{2} = \sin(\frac{\pi}{4})
|
-18,986
|
1/5 = \frac{1}{49\cdot \pi}\cdot C_x\cdot 49\cdot \pi = C_x
|
27,706
|
\frac{1}{f x} f = 1/(\frac{x}{f} f)
|
-25,222
|
z^{l + \left(-1\right)} \cdot l = \frac{\mathrm{d}}{\mathrm{d}z} z^l
|
25,713
|
{p \choose p} p^x = p^x
|
-6,478
|
\frac{2}{3 \cdot r + 3 \cdot (-1)} = \frac{2}{3 \cdot (r + (-1))}
|
7,282
|
\cos(h + z) = \cos{z}\cdot \cos{h} - \sin{h}\cdot \sin{z}
|
44,537
|
(-1) + 4^{1000} = 2^{2000} + (-1)
|
-17,810
|
11 + 10\cdot (-1) = 1
|
1,529
|
\sin{p} \cdot \cos{\pi/2} + \sin{\pi/2} \cdot \cos{p} = \sin(p + \frac12 \cdot \pi)
|
-25,029
|
-z \cdot 2 + 8/3 \cdot z \cdot z \cdot z - z^5 \cdot 32/5 + z^7 \cdot \frac{128}{7} + \dots = \arctan{-z \cdot 2}
|
4,631
|
-b^2 + x^2 = (x - b)\times (b + x)
|
15,462
|
z + 2 = \frac{1}{z + 2(-1)}(z + 2) (z + 2(-1)) = \frac{z^2 + 4\left(-1\right)}{z + 2(-1)}
|
-12,366
|
5\cdot \sqrt{6} = \sqrt{150}
|
19,620
|
\cos(x)*\sin\left(x\right) = \sin(2*x)/2
|
8,447
|
6 + z^2 + 6\cdot z = 3\cdot (-1) + z^2 + 4\cdot z + 9 + 2\cdot z
|
-26,152
|
2 \cdot 16^{\frac{1}{2} \cdot 3} - 2 \cdot 4^{\frac{3}{2}} = 128 + 16 \cdot (-1) = 112
|
-3,653
|
\frac{18 \times p^4}{21 \times p^5} = \frac{p^4}{p^5} \times 18/21
|
-20,383
|
\frac{1}{9*(-1) + k}*(k + 9*\left(-1\right))*(-4/9) = \frac{36 - k*4}{k*9 + 81*(-1)}
|
50,155
|
6442450944 = 2^{31}*3
|
5,245
|
\cos{\dfrac{\pi*2}{5}} = \cos{8\pi/5}
|
-24,815
|
2445\cdot (-1) - 3 = -2448
|
6,997
|
gx + xd = x*(g + d)
|
12,589
|
\frac{1}{6} + \frac16 = \frac26
|
3,741
|
1/\left(1/\left(\frac1R\right)\right) = 1/R
|
-20,132
|
-\frac{1}{9}\cdot 2\cdot \frac{10\cdot \left(-1\right) + z}{10\cdot \left(-1\right) + z} = \frac{20 - 2\cdot z}{z\cdot 9 + 90\cdot (-1)}
|
-23,158
|
-2/3 (-\frac198) = 16/27
|
12,576
|
\tfrac{1}{C \cdot A} = \dfrac{1}{A \cdot C}
|
-9,241
|
y*35 = y*5*7
|
14,331
|
m_1 = 0.6711 m_2 = 0.9559\Longrightarrow m_1 \lt m_2 < 3 m_1
|
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