PsychoCom

### Questions (10)

 9 How does the Cantor's diagonal argument that $(0,1)$ is uncountable deals with the fact some real numbers have two different decimal expansions? 6 Every group homomorphism from $(\mathbb{Q}, +)$ to $(\mathbb{Q}, \times)$ is the trivial map. 4 Does $x^3 - \frac{m}{n}\sqrt{5}x - 1$ has rational root? 1 $m$ is prime if some integer has order $m-1$ modulo $m$ 1 Prove that for any eigenvalue, its eigenspace is in direct sum with the sum of all other eigenspaces of distinct eigenvlaues.

### Reputation (124)

 +20 Does $x^3 - \frac{m}{n}\sqrt{5}x - 1$ has rational root? +5 $m$ is prime if some integer has order $m-1$ modulo $m$ +30 Every group homomorphism from $(\mathbb{Q}, +)$ to $(\mathbb{Q}, \times)$ is the trivial map. +5 Prove that for any eigenvalue, its eigenspace is in direct sum with the sum of all other eigenspaces of distinct eigenvlaues.

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### Tags (19)

 0 linear-transformations × 4 0 group-theory × 2 0 linear-algebra × 4 0 abstract-algebra × 2 0 elementary-set-theory × 2 0 finite-groups 0 matrices × 2 0 modular-arithmetic 0 polynomials × 2 0 number-theory

### Accounts (3)

 Mathematics 124 rep 99 bronze badges Cross Validated 11 rep 22 bronze badges Stack Overflow 7 rep 33 bronze badges