Datasets:
LiamYo
/
MathWritingHandwritten

Dataset card Data Studio Files
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115 values
[\begin{matrix}1&2\\ 1&1\end{matrix}]
000000100
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
80^{80^{80^{80^{...}}}}
000000101
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
{k^{l}}^{f}
000000102
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
P_{cr}=\alpha\frac{\lambda^{2}}{4\pi n_{0}n_{2}}
000000103
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
rN(1-\frac{N}{K})=H
000000104
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{16}{5}\sqrt{\frac{2}{7\pi}}
000000105
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\int_{-r}^{r}|y-s|dx
000000106
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
a^{a^{-^{-^{a^{a}}}}}
000000107
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
H_{(1-X)}=\frac{\beta-1}{2\beta-1}
000000108
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
Re_{p}
000000109
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
<<<
000000110
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\tilde{\gamma}(0)=p
000000111
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
x\leftarrow x+0
000000112
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
E=\frac{sc^{9}}{\sqrt{1+\frac{d^{9}}{c^{9}}}}
000000113
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
w_{1}^{i}=\frac{1}{N}
000000114
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(t,y)\in[0,T]\times R^{m}
000000115
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
V=\frac{E*G*U}{O*R}
000000116
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\partial^{2}f/\partial x^{2}
000000117
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\int_{c(r)}R(z)dz=0
000000118
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
H=kA\frac{T_{H}-T_{L}}{L}
000000119
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\begin{matrix}4\\ 2\end{matrix})=6
000000120
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\nu,\mu
000000121
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\overline{O_{L}P}
000000122
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
{{3^{\sqrt{9}}}^{468}}^{(\frac{431}{38})^{7}}
000000123
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\frac{7}{167}}{(454^{7}+6)}
000000124
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
n\cdot sin(\frac{1}{n})
000000125
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\beta<min(R,2\sqrt{R})
000000126
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
t=\frac{e}{s_{e}}
000000127
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\nabla B_{z}=\frac{dB_{z}}{dA}\nabla A
000000128
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
M=(\begin{matrix}0&0\\ 1&0\end{matrix})
000000129
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
J=-M(\frac{d}{dx})\frac{df}{dc}
000000130
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{b-a}{2}(f_{0}+f_{1})
000000131
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\mu(\tilde{X}\cap\tilde{Y})=0
000000132
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{dV_{r}}{dt}
000000133
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
exp(m,n)=m^{n}
000000134
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
-2x+5<x+3
000000135
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
i_{1}^{\prime}=\frac{i_{1}\cdot vt_{1}}{\sqrt{1\cdot\frac{v^{8}}{n^{8}}}}
000000136
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\underline{x}=(x_{1},...,x_{d})
000000137
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\psi\rightarrow\varphi
000000138
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\begin{matrix}m+n\\ m\end{matrix})
000000139
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
{7^{112}}^{\frac{\sqrt{5}}{\sqrt{10}}}
000000140
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sqrt{g/l}
000000141
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\begin{matrix}x\\ k\end{matrix})
000000142
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
K/BB=\frac{K}{BB}
000000143
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sqrt{m}
000000144
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
[\begin{matrix}3&4&4\\ 4&5\\ 6&7\end{matrix}]
000000145
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
q=K\sqrt{p}
000000146
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
x^{n-m}=\frac{x^{n}}{x^{m}}
000000147
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
[\begin{matrix}ac\\ bd\\ 0\end{matrix}]
000000148
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\hat{q}_{o}
000000149
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|x[n]|
000000150
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
O(\sqrt{logn_{i-1}})
000000151
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
1-\frac{2}{\sqrt{5}}
000000152
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
{238^{412}}^{\frac{132^{246}}{293}}
000000153
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
a\cdot\frac{m}{s}:=\frac{am}{s}
000000154
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(x)O(\underline{x}:G)
000000155
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\theta=\theta_{o}
000000156
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\tilde{X}=f(Y)
000000157
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{dS}{dt}=N\cdot v
000000158
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
II_{\infty}
000000159
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sqrt{\frac{5}{126}}
000000160
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\begin{matrix}k-1\\ D-1\end{matrix})
000000161
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\int_{S}FdS
000000162
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\partial logB_{\nu}(T)}{\partial log\nu}\simeq2
000000163
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
e^{j\omega t}
000000164
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
z=\frac{h}{\sqrt[8]{\cdot\frac{u_{1}}{5}}}
000000165
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
{\prod_{i}}^{\prime}G_{i}
000000166
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
s\{\begin{matrix}3\\ 3\end{matrix}\}
000000167
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
A_{0}=aA^{*}
000000168
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\frac{\frac{3}{492}}{149})^{{6^{202}}^{8}}
000000169
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
368+8-\frac{483}{\sqrt{206}}
000000170
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
p=\frac{RT}{\underline{V}}
000000171
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{m}{\sqrt{5-\frac{y^{8}}{c^{8}}}}
000000172
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
3\sqrt{2}
000000173
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\frac{\frac{3}{\sqrt{1}}}{447}}{4^{7}}
000000174
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
g(x)=5\sqrt{x}
000000175
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
{\sqrt{6}+333^{10}}^{{9^{140}}^{10}}
000000176
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\Rightarrow b=\frac{n}{2n-1}
000000177
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{D_{\odot}^{2}}{2\mu_{0}r_{c}^{6}}=nmv^{2}
000000178
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
g=(\begin{matrix}A&B\\ C&D\end{matrix})
000000179
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\hat{\nu}_{i}
000000180
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
2(\begin{matrix}n\\ j\end{matrix})
000000181
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
r_{N}^{k}(m)<cn^{\frac{N}{k}-1}
000000182
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\partial X_{i}}{\partial P_{Y}}>0
000000183
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
1-C^{2}
000000184
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\hat{\beta}=(\overline{y/x})
000000185
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
C/D\ge20
000000186
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\begin{matrix}4\\ 2\end{matrix})
000000187
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{du}{dy}
000000188
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{mn(n+1)}{mn(n+1)+2np}
000000189
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
2^{2^{2^{2^{74}}}}
000000190
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{3}{2}\frac{F}{V_{0}}
000000191
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
L(s,E)=\prod_{p}L_{p}(s,E)^{-1}
000000192
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
y=\sqrt[3]{x}
000000193
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sigma(t)=(\frac{1}{1-t},0)
000000194
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{(\frac{9}{6}+309)}{\frac{10}{10}}
000000195
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{6(90-\pi^{4})}{5(\pi^{2}-6)^{2}}
000000196
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
X\sim Benini(\alpha,0,\sigma)
000000197
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
M=(\begin{matrix}1&-1\\ 0&0\end{matrix})
000000198
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
D=\frac{k_{B}T}{f}
000000199
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar