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Omni-MATH / An infinite sequence x₀,x₁,x₂,… of real numbers is said to be [b]bounded[/b] if there is a constant C such that , vert x_{i} vert leq C, for every i≥0. Given any real number …

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problem

An infinite sequence x0,x1,x2,… \,x_{0},x_{1},x_{2},\ldots \, of real numbers is said to be [b]bounded[/b] if there is a constant C \,C\, such that $ \, \vert x_{i} \vert \leq C\,$ for every i≥0 \,i\geq 0. Given any real number a>1, \,a > 1,\, construct a bounded infinite sequence x0,x1,x2,… x_{0},x_{1},x_{2},\ldots \, such that \[ \vert x_{i} \minus{} x_{j} \vert \vert i \minus{} j \vert^{a}\geq 1 \] for every pair of distinct nonnegative integers i,j i, j.
Plain-text mathematical notation (without MathML)
An infinite sequence  x₀,x₁,x₂,…  of real numbers is said to be [b]bounded[/b] if there is a constant  C  such that $ \, \vert x_{i} \vert \leq C\,$ for every  i≥0. Given any real number  a>1,  construct a bounded infinite sequence x₀,x₁,x₂,…  such that
\[ \vert x_{i} \minus{} x_{j} \vert \vert i \minus{} j \vert^{a}\geq 1
\]
for every pair of distinct nonnegative integers i,j.
Original LaTeX notation
An infinite sequence $ \,x_{0},x_{1},x_{2},\ldots \,$ of real numbers is said to be [b]bounded[/b] if there is a constant $ \,C\,$ such that $ \, \vert x_{i} \vert \leq C\,$ for every $ \,i\geq 0$. Given any real number $ \,a > 1,\,$ construct a bounded infinite sequence $ x_{0},x_{1},x_{2},\ldots \,$ such that
\[ \vert x_{i} \minus{} x_{j} \vert \vert i \minus{} j \vert^{a}\geq 1
\]
for every pair of distinct nonnegative integers $ i, j$.

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Source and history

task_id
d82d2c39-6054-5e0b-a7a7-5d3a20aa184a
task_key
test--d82d2c39-6054-5e0b-a7a7-5d3a20aa184a
task_revision_id
1
config / split
/ test

Official source

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