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Omni-MATH / Find all positive real numbers t with the following property: there exists an infinite set X of real numbers such that the inequality max{|x−(a−d)|,|y−a|,|z−(a+d)|}>td holds for al…

Problem

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problem

Find all positive real numbers tt with the following property: there exists an infinite set XX of real numbers such that the inequality max{|x−(a−d)|,|y−a|,|z−(a+d)|}>td \max\{|x-(a-d)|,|y-a|,|z-(a+d)|\}>td holds for all (not necessarily distinct) x,y,z∈Xx,y,z\in X, all real numbers aa and all positive real numbers dd.
Plain-text mathematical notation (without MathML)
Find all positive real numbers t with the following property: there exists an infinite set X of real numbers such that the inequality max{|x−(a−d)|,|y−a|,|z−(a+d)|}>td holds for all (not necessarily distinct) x,y,z∈X, all real numbers a and all positive real numbers d.
Original LaTeX notation
Find all positive real numbers $t$ with the following property: there exists an infinite set $X$ of real numbers such that the inequality \[ \max\{|x-(a-d)|,|y-a|,|z-(a+d)|\}>td\] holds for all (not necessarily distinct) $x,y,z\in X$, all real numbers $a$ and all positive real numbers $d$.

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Source and history

task_id
51053255-7b9e-5f75-9586-b192221bb135
task_key
test--51053255-7b9e-5f75-9586-b192221bb135
task_revision_id
1
config / split
/ test

Official source

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