4 ms·
I think it really is exactly a power, as long as `b` is allowed to be any real number.
by sapiogram 3y ago
I think it really is exactly a power, as long as `b` is allowed to be any real number.
- FartyMcFarter 3y agoEvery positive number is exactly a power if you allow that.
- c7b 3y agoEvery positive number is in fact (uncountably) infinitely many powers in this case.
- kdmccormick 3y agoYup. I got hung up on that too. I think the article could have better stated it as: For every natural n, there exists a natural b, such that: n! ≈ b^n I don't quite know the precise criteria for "≈" here, that's a bit beyond my understanding of the article...
- throwawaymaths 3y agoHe also mis-typesets it as = on the same line! Very confusing.
- gowld 3y ago≈ is a loose approximation. The fact is that `e * (n!)^(1/n)` is quite close to `n`. But John didn't factor out the `e`, causing the confusion in this HN post's threads.
- ftxbro 3y agoso you're saying the title is accurate
- FartyMcFarter 3y agoIt's either inaccurate or trivial depending on how you interpret it: - If you only allow the base to be an integer, then it's inaccurate. - If you allow the base to be a real number, then you're really just saying "every factorial is a positive number", which is a trivial fact if you know what a factorial is. Either way it's a bad title IMO.
- ftxbro 3y agoyes it's clickbait, which is sad because that blogger is an OG computational science popularizer EDIT: whoever is downvoting me, the article title is objectively clickbait