7 How many 7-digit phone numbers are possible, assuming that the first digit can’t be a 0 or a 1 7 What is the name of this function property? 7 Inverse of x^x? 7 Theorem: Let $n$ be an integer. If $n^2$ is even, then $n$ is even 7 How many ways can you arrange 3 pennies and 2 nickels in a line?

### Reputation (6,501)

 +15 What do you call a graph with two nodes but no edge connecting two nodes? +20 Is logical equivalence in itself a proposition? +10 Is the multiplicative identity unique in a unit ring? +10 Better proof for $\frac{1+\cos x + \sin x}{1 - \cos x + \sin x} \equiv \frac{1+\cos x}{\sin x}$

### Questions (87)

 16 Is Pythagoras' Theorem a theorem? 12 Notation: Is $(\Delta x)^2 = \Delta x^2$? 7 Better proof for $\frac{1+\cos x + \sin x}{1 - \cos x + \sin x} \equiv \frac{1+\cos x}{\sin x}$ 7 Coefficients of the characteristic polynomial 7 Defining the Cosine Function from First Principles, intuitively

### Tags (182)

 39 combinatorics × 20 22 functions × 9 37 calculus × 23 19 sequences-and-series × 14 33 algebra-precalculus × 14 19 proof-verification × 12 26 integration × 11 17 linear-algebra × 29 23 abstract-algebra × 18 14 summation × 11

### Bookmarks (4)

 198 How to read a book in mathematics? 29 When functions commute under composition 11 Ring homomorphism with $\phi(1_R) \neq1_S$ 3 Union of Subgroups