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Omni-MATH / Let (a_(n))_(n≥0) and (b_(n))_(n≥0) be two sequences of natural numbers. Determine whether there exists a pair (p,q) of natural numbers that satisfy …

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problem

Let (an)n≥0(a_n)_{n\geq0} and (bn)n≥0(b_n)_{n \geq 0} be two sequences of natural numbers. Determine whether there exists a pair (p,q)(p, q) of natural numbers that satisfy p<q and ap≤aq,bp≤bq.p < q \quad \text{ and } \quad a_p \leq a_q, b_p \leq b_q.
Plain-text mathematical notation (without MathML)
Let (a_(n))_(n≥0) and (b_(n))_(n≥0) be two sequences of natural numbers. Determine whether there exists a pair (p,q) of natural numbers that satisfy
p<q  and  a_(p)≤a_(q),b_(p)≤b_(q).
Original LaTeX notation
Let $(a_n)_{n\geq0}$ and $(b_n)_{n \geq 0}$ be two sequences of natural numbers. Determine whether there exists a pair $(p, q)$ of natural numbers that satisfy
\[p < q \quad \text{ and } \quad  a_p \leq a_q, b_p \leq b_q.\]

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Source and history

task_id
9c43c362-3a25-5c45-bf1c-597359b12d22
task_key
test--9c43c362-3a25-5c45-bf1c-597359b12d22
task_revision_id
1
config / split
/ test

Official source

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