15 Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true? 14 Tips for writing proofs 10 How to tell if I'm good enough for graduate school? 9 Clear explanation about uniform continuity. 8 How do you show that $e^{-1/x^2}$ is differentiable at $0$?

Reputation (3,031)

 +30 How do you show that $e^{-1/x^2}$ is differentiable at $0$? +10 Tips for writing proofs +10 Where to go from here…graduate school +10 dimension of the subspace $W$ of $10\times 10$ matrices , $W=\{[a_{ij}]: a_{ij}=0\text{ if i is even }\}$

Questions (5)

 3 Smoothing continuous functions 2 Generalization of Tonelli's Theorem for Series 2 invariance of π [duplicate] 0 Uncountable sets on $(0,\infty)$ also uncountable on $[b,\infty]$ for some $b > 0$ 0 Counter example needed -series/sequences

Tags (100)

 58 soft-question × 14 19 education × 6 42 real-analysis × 36 19 abstract-algebra × 4 34 calculus × 34 18 continuity × 3 31 linear-algebra × 15 17 proof-writing × 5 24 advice × 5 15 examples-counterexamples