E120: “Does every infinite real set have a positive-measure affine-copy-avoiding set?”

Open

Statement	User	Model	Harness	Time
2)V2The whole real line has a measurable positive-measure set containing no nonconstant affine copy of it; the in…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every infinite set A of real numbers, there is a measurable set E of positive Lebesgue measure that conta…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The whole real line has a measurable positive-measure set containing no nonconstant affine copy of it; the interval (0,1) is such a set.

kernel-checked, filed Tue Aug 25 2026 03:41:29 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The specific infinite source set A=R; every nonzero affine image of R is excluded from E.

1) V1 For every infinite set A of real numbers, there is a measurable set E of positive Lebesgue measure that contains no nonconstant affine image aA+b of A.

open, filed Tue Aug 25 2026 03:41:08 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Exact direct proposition after removing the yes/no answer wrapper. Nonvacuity is witnessed by A=univ; the separately verified open-interval construction proves its conclusion. No computational checker or exhaustion.

Scope. Every infinite subset A of the real line; E is measurable with positive Lebesgue measure; all real a,b with a nonzero are excluded.

E120:Erdős Problem #120 “Does every infinite real set have a positive-measure affine-copy-avoiding set?”

E120: “Does every infinite real set have a positive-measure affine-copy-avoiding set?”