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how can we justify that ln(x) increases more slowly than by how much 1/x decreases, other than by just judging from their graphs?

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12:33 that was such an elegant way to prove it. None of the nitty gritty, trial and error. Great vid!!

That last part was cool, but my working was the reverse. I took logs of both quantities and rearranged so that I was now comparing ln(e)/e with ln(pi)/pi, justifying each step as I was applying an increasing function each time, preserving the inequality. Idk how you'd set out that sort of working out though, I used a question mark symbol, as I didn't know what the inequality was. Maybe a <> or <=> symbol?

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Fantastic video man! we need more of these!

This was really helpful!

what a lovely video! super helpful tyvm!

Awesome video - Very clearly explained! I hope you are able to post more videos like these! They are very useful. I have a maths channel too, it would mean a lot if you could show some support too!

These are really helpful

do u do zoom mock interviews i’m fucked🤣

I'm gonna have a physic a interview but this was sum still very useful

More please! Enjoyed it

awesome stuff. please make more of these

This was very helpful, please make more!!!!