Fake proof that $1=0$ using the product law for limits
116423
What is wrong with the argument $1 = \lim_{n\to \infty} n/n = \lim_{n\to\infty} (1/n+1/n+\dotsb+1/n) = 0 $?
115514
Is the product $\prod_{k=1}^\infty \frac{2^k-1}{2^k}$ necessarily $0$?
13533
Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
158343
how to prove an element is non-zero in a tensor-product
46990
$\lim_{x\to0}\frac{e^x-1-x}{x^2}$ using only rules of algebra of limits.
85269
Proof that limit of (lnx)/x = 0 without LHopital
53688
How can one prove that $\lim_{n \to \infty}a^{1/n}=1$ for every $a>0$?
60217
Proof: Series converges $\implies $ the limit of the sequence is zero
5728
How to prove $\lim_{n \to \infty} \sqrt{n}(\sqrt[n]{n} - 1) = 0$?
122076
A one line proof that one is zero using Mathematica 10
49928
Proving limit of a sum
30860
Prove that $f(x)=0$ in $[-1,1]$.
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
23557
Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$
147528
Where's the error in this $2=1$ fake proof?
3979
Limit comparison test proof
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$