From discrete to continuous: Monochromatic 3-term arithmetic progressions
From discrete to continuous: Monochromatic 3-term arithmetic progressions
We prove a known 2-coloring of the integers <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket upper N right-bracket colon-equal StartSet 1 comma 2 comma 3 comma ellipsis comma upper N EndSet"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy="false">]</mml:mo> <mml:mo>≔</mml:mo> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo …