Datasets:
LiamYo
/
MathWritingHandwritten

Dataset card Data Studio Files
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115 values
2+\sqrt{2}+\sqrt{6}
000000600
/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\sqrt{\frac{2+b^{2}}{2}}
000000601
/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,y\notin H_{3},H_{4}
000000602
/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{2}{10}}{8^{366}}
000000603
/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=\frac{NIA}{L}
000000604
/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{c}
000000605
/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
\mathbb{L}
000000606
/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{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}
000000607
/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{p}=0
000000608
/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^{7^{7^{7^{7}}}}-5
000000609
/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_{2}=a-\frac{a\cdot b}{b\cdot b}b
000000610
/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
1-5/3+4^{466}
000000611
/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{dB}{dG}=0
000000612
/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_{l,m}^{(E)}=\frac{i}{k}\nabla\times B_{l,m}^{(E)}
000000613
/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{wc^{0}}{\sqrt{1+\frac{d^{0}}{c^{0}}}}
000000614
/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=x
000000615
/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
(b-c))
000000616
/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}9\\ 6\end{matrix})
000000617
/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+1)p-1\notin\mathbb{Z}
000000618
/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=sup_{|z|\le R}Ref(z)
000000619
/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\circ X
000000620
/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_{i}=\frac{\hat{p}_{i}\cdot\overline{p}}{\sqrt{\frac{\overline{p}(5\cdot\overline{p})}{r_{i}}}}
000000621
/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=g_{00}\gamma
000000622
/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|_{U}:U\rightarrow V
000000623
/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{4}
000000624
/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
\mathbb{F}
000000625
/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{N}(s)=L\{N(t)\}
000000626
/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=\lceil log_{2}n+1\rceil
000000627
/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=\frac{ln(1-P)}{ln(1-f)}
000000628
/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_{g}=\frac{2\pi\Delta f}{\Delta k}=\frac{\Delta\omega}{\Delta k}
000000629
/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{-1}
000000630
/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}\times\sqrt{6}
000000631
/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(nlogn)
000000632
/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 a(x)d\mu
000000633
/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=\frac{3t}{\sqrt{10}}+3k
000000634
/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 u}{\partial n}|_{\Gamma_{2}}=g
000000635
/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
F_{y}-\frac{d}{dt}F_{y^{\prime}}=0
000000636
/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{Z}e^{T}|\phi\rangle
000000637
/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\rightarrow\frac{x-\xi}{\omega}
000000638
/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=\frac{\partial^{2}V}{\partial Q^{2}}
000000639
/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 d^{3}xJ^{0}
000000640
/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=\overline{x}
000000641
/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{m_{8}v}{\sqrt{7-\frac{v^{5}}{u^{5}}}}
000000642
/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_{a}^{b}f(x)dv(x)
000000643
/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^{433}\cdot111+\sqrt{5}^{381}
000000644
/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{f}:X\rightarrow M_{f}
000000645
/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\ge\sum_{i=1}^{n}(p_{i}\cdot x_{i})
000000646
/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^{\cdot\frac{(F\cdot M)^{0}}{0{(s_{F})}^{0}}}
000000647
/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{dZ(t)}{dt}
000000648
/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{dF}{dL}
000000649
/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^{7^{7^{7^{7^{7}}}}}+3
000000650
/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{dy}{dx}=\frac{x}{y}
000000651
/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 C
000000652
/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=n-r+1}^{n}i
000000653
/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=\prod_{i}{p_{i}}^{e_{i}}
000000654
/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}a&b\\ b&c\end{matrix})
000000655
/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(t)=L\frac{di(t)}{dt}
000000656
/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}
000000657
/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
f:\mathbb{R}\rightarrow\mathbb{R}_{0}^{+}
000000658
/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{T}_{f}
000000659
/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=2rsin(\frac{\theta}{2})
000000660
/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}n+2\\ 2\end{matrix})-2n-1
000000661
/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^{\frac{1}{2}}=\sqrt{2}
000000662
/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\\ 5\end{matrix}\}
000000663
/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_{i}=a+i\Delta x=\frac{2i}{n}
000000664
/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_{0}^{\infty}f(x)dx\approx-\frac{\pi}{2}
000000665
/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=\frac{ed}{1+esin\theta}
000000666
/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_{\omega_{1},\omega}(Q)
000000667
/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=N!/\prod_{i}N_{i}!
000000668
/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
ss\{\begin{matrix}2\\ 2\end{matrix}\}
000000669
/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\psi}{dt}=\frac{T_{x}}{C\omega sin\epsilon}
000000670
/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/\sqrt{\epsilon_{0}\mu_{0}}
000000671
/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
(Im(\Gamma(\omega))<0)
000000672
/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
\sum_{n=1}^{\infty}\frac{sin\frac{x}{n}}{n}
000000673
/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_{1}}{a}\le2
000000674
/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=\int xcos(x)dx
000000675
/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_{4}^{\prime}=\frac{y_{4}-\frac{z}{c^{2}}k_{4}}{\sqrt{4-\frac{z^{2}}{c^{2}}}}
000000676
/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}11\\ 5\end{matrix})
000000677
/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\cdot10^{{6^{1}}^{1}}
000000678
/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
lim_{n\rightarrow\infty}(2^{n})^{\frac{1}{n}}=2
000000679
/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{q_{1}q_{2}}{4\pi\epsilon_{0}|r|}
000000680
/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
\xi_{1}(s)=s\zeta(s+1)
000000681
/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
mv\approx\frac{E}{c}
000000682
/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_{V_{1}}^{V_{2}}PdV
000000683
/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=\{x|x\notin x\}
000000684
/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^{398}}^{\frac{(4-2)}{10}}
000000685
/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
0.5\sqrt{N}
000000686
/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:=L(\underline{a}_{1},...,\underline{a}_{r})
000000687
/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=\frac{1}{2}absinC
000000688
/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^{4}+3125=125x^{2}
000000689
/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{g}
000000690
/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{dE}{dx}=0
000000691
/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{\partial P}{\partial V})_{S}
000000692
/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{1}{2}\nu^{T}\sigma\sigma^{T}\nu}
000000693
/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{7^{258}}{270})^{\frac{6}{50}}
000000694
/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^{\theta_{\eta}}
000000695
/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
((4+357)+\frac{6}{26})
000000696
/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(n)=\prod_{k=1}^{n}f(k)
000000697
/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{\cdot}{n})
000000698
/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
\alpha_{2}=\frac{1}{2}+m
000000699
/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