6,030 reputation
21439
bio website plus.google.com/…
location Cambridge, United Kingdom
age 22
visits member for 2 years, 9 months
seen 3 hours ago

I'm a silly ass.


3h
comment A simple mathematical induction proof.
Yes - well done. That's the right answer.
7h
comment A simple mathematical induction proof.
@HMPARTICLE Yes, that's basically the right idea. Try and write the whole proof out in full now!
10h
reviewed Approve Size of the orbits of a normal subgroup
12h
comment Prove that $\lim_{x \to 0 } \frac{\ln(x+1)}{x} = 1$
L'Hôpital's rule is redundant here. In order to use it, you need to know that the derivative of $\ln(t)$ is $\frac1t$. But if you know that, then you can observe that the OP's limit is precisely $\frac{d}{dx}(\ln(x))$ evaluated at $1$, giving you $\frac11=1$.
13h
reviewed No Action Needed Moving average with negative values
13h
reviewed Close Generalization of linear approximation?
13h
reviewed Leave Open Find a probability of $n$ event happening from $m$ types
13h
reviewed Leave Open Prove that $\lim_{x \to 0 } \frac{\ln(x+1)}{x} = 1$
13h
reviewed Edit Complex Limit Without L'hopital's
13h
revised Complex Limit Without L'hopital's
improved formatting
14h
comment Why the Riemann hypothesis doesn't imply Goldbach?
It might be worth updating this to include more recent results on the weak Goldbach conjecture (even though they are unconditional on RH).
14h
reviewed Reopen Modifying recursion matching result
14h
reviewed Reopen What is $\tau(A)$ of components of $G \backslash A$, where $A \subseteq V$?
14h
reviewed Looks OK Blue eyes: a logic puzzle
14h
reviewed Leave Open How do we establish the existence of fundamental matrix of a Markov chain?
14h
reviewed Close How many digits are there in 100!?
14h
reviewed Reject Extension of nonisomorphic simple objects
14h
reviewed Reject Comparing up-arrow's
14h
comment A simple mathematical induction proof.
You're very close though!
14h
comment A simple mathematical induction proof.
@HMPARTICLE Hint: suppose $f(i)=1000$ for $i=1,\dots,n$ and $f(n+1)=1$. Does setting $M=f(n+1)$ work in that case? And how are you going to use the fact that the proposition is true for $n$ to deduce that it's true for $n+1$?