Consider the following polynomials: $$ f_1(n_1, m_1) = 30n_1m_1 + 23n_1 + 7m_1 + 5\\ f_2(n_2, m_2) = 30n_2m_2 + 17n_2 + 13m_2 + 7\\ f_3(n_3, m_3) = 30n_3m_3 + 23n_3 + 11m_3 + 8\\ f_4(n_4, m_4) = 30n_4m_4 + 11n_4 + 29m_4 + 11\\ f_5(n_5, m_5) = 30n_5m_5 + 29n_5 + 17m_5 + 16\\ f_6(n_6, m_6) = 30n_6m_6 + 19n_6 + 7m_6 + 4\\ f_7(n_7, m_7) = 30n_7m_7 + 31n_7 + 13m_7 + 13\\ $$ where each $n_1, m_1,..., n_7, m_7 \in \mathbb{N}$

How can I prove that $\left\vert{\:\mathbb{N} \setminus (f_1 \cup f_2\: \cup\: ... \cup \:f_7)\:}\right\vert = \infty$?

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