benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / For x∈(0,1) let y∈(0,1) be the number whose n-th digit after the decimal point is the 2^(n)-th digit after the decimal point of x. Show that if x is rational then so is y. [i]

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

For x∈(0,1) x \in (0, 1) let y∈(0,1) y \in (0, 1) be the number whose n n-th digit after the decimal point is the 2n 2^{n}-th digit after the decimal point of x x. Show that if x x is rational then so is y y. [i]
Plain-text mathematical notation (without MathML)
For x∈(0,1) let y∈(0,1) be the number whose n-th digit after the decimal point is the 2^(n)-th digit after the decimal point of x. Show that if x is rational then so is y.

[i]
Original LaTeX notation
For $ x \in (0, 1)$ let $ y \in (0, 1)$ be the number whose $ n$-th digit after the decimal point is the $ 2^{n}$-th digit after the decimal point of $ x$. Show that if $ x$ is rational then so is $ y$.

[i]

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
fdd2f429-a0b7-57be-9b31-6405bc9bdd15
task_key
test--fdd2f429-a0b7-57be-9b31-6405bc9bdd15
task_revision_id
1
config / split
/ test

Official source

initial import