\(\mathrm{\SunQuarTeX}\) Example - enart

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Abstract

This is an abstract.

1 First

This is a reference [1, p. 1].

\(\mathrm{\SunQuarTeX}\) is powered by Quarto and \(\mathrm{\LaTeX}\).

Example 1 Prove that \[ \mathbb R \times \mathbb N \approx \mathbb N \times \mathbb R \approx \mathbb R \]

Proof

Proof. Obvious as follows \[ \mathbb R \approx \mathbb R \times 2 \preccurlyeq \mathbb R \times \mathbb N \preccurlyeq \mathbb R \times \mathbb R \approx \mathbb R \implies \mathbb R \times \mathbb N \approx \mathbb N \times \mathbb R \approx \mathbb R \]

2 Second

\(L_i \times C_j\)	\(2\)	\(\mathbb N\)	\(\mathbb R\)
\(2\)	\(4\)	\(\mathbb N\)	\(\mathbb R\)
\(\mathbb N\)	\(\mathbb N\)	\(\mathbb N\)	?
\(\mathbb R\)	\(\mathbb R\)	?	\(\mathbb R\)

(a) Cartesian (unsolved)

\(L_i^{C_j}\)	\(2\)	\(\mathbb N\)	\(\mathbb R\)
\(2\)	\(4\)	\(\mathbb R\)	\(2^{\mathbb R}\)
\(\mathbb N\)	\(\mathbb N\)	?	?
\(\mathbb R\)	\(\mathbb R\)	?	?

(b) Power (unsolved)

Table 1: Some Cardinality Results

3 Code

#include<bits/stdc++.h>
using namespace std;

int main(){
    return 0; // 返回 0
}

example : (∀ x, p x → r) → ((∃ x, p x) → r) := by
  intro h ⟨a, hpa⟩ -- you may also `rcases` explicitly
  exact h a hpa

References

[1]

Y. Taigman, M. Yang, M. Ranzato, and L. Wolf, “Closing the gap to human-level performance in face verification. deepface,” in Proceedings of the IEEE computer vision and pattern recognition (CVPR), p. 6.