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Showing posts from January, 2023

Let

K

be a finite field.

1 + 1 = 0

in K if and only if for any

f \in K [x]

such that the degree of

f

is more or equal to 1, the polynomial

f (X^{2})

is a reducible polynomial.

Clearly the set of continuous function

C [a, b]

is a vector space. Now, we have to prove that the function

{| | \cdot | |}_{\infty} : C [a, b] \to R

such that

{| | f | |}_{\infty} = max_{a \leq x \leq b} | f (x) |

for every function

f \in C [a, b]

is really a norm.

Generate a random species.