trustmebro.to/r/…
✓ checked
trust me, bro:
here is the receipt.
the claim

All irrational numbers are transcendental numbers.

the verdict
REFUTED
the evidence says no
Recorded sources
0 sources for · 3 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

Is it true that all irrational numbers are transcendental numbers?

No. Not all irrational numbers are transcendental; some, like the square root of two, are algebraic irrational numbers.

Verdict: REFUTED · 0 sources for, 3 against · Last checked

How claims like this are judged

Judged against reference works: claims of this kind are settled by reference works, not journal abstracts.

Evidence against · 3
arXiv: arXiv: On the complexity of algebraic number I. Expansions in integer bases
Mentions 'irrational algebraic number', proving not all irrational numbers are transcendental.
Get citation
arXiv: arXiv: On the complexity of algebraic number I. Expansions in integer bases. (n.d.). arXiv. https://arxiv.org/abs/math/0511674

See more details
More against · 2
Wikibooks: Wikibooks: Number Theory/Irrational Rational and Transcendental Numbers
States that √2 is an algebraic number (but irrational), refuting the claim.
Get citation
Wikibooks: Wikibooks: Number Theory/Irrational Rational and Transcendental Numbers. (n.d.). Wikibooks. https://en.wikibooks.org/wiki/Number_Theory/Irrational_Rational_and_Transcendental_Numbers

Wikipedia: Wikipedia: Transcendental number
Explicitly states 'Not all irrational numbers are transcendental.'
Get citation
Wikipedia: Wikipedia: Transcendental number. (n.d.). Wikipedia. https://en.wikipedia.org/wiki/Transcendental_number

also asked as
  • Are all irrational numbers also transcendental numbers?
  • Do irrational numbers always turn out to be transcendental?
  • Is every irrational number considered a transcendental number?
  • Can we say that all irrational numbers are transcendental?
Receipt History
Anyone with this link can read the claim and its public receipt, including any personal information in that text. Open permanent receipt.
Check your own claim
Challenge the receipt
Requests are recorded for review. This does not start an automatic check or guarantee a response time.

Citation formatting by citeproc-js (Frank Bennett) and the Citation Style Language project. Source and licenses.

This receipt is an automated verdict against our published method · not an opinion about any author or publication.
Terms · Privacy · How verdicts work