List questions from proof-verification

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List Question

Linearly Indept set of n vectors implies size of vector space to be at least n.

Lusin's theorem on arbitrary measure space

Fundamental subfield of a field $F$

$(a) = R$ if and only if a is a unit.

Showing that the equation $x_i - \sum_{j=1}^\infty a_{ij}x_j = b_i$ has a unique solution.

W1 + W3 = W2 + W3. Then W1 = W2

Examining the following Series for convergence with proof

Set of all sequences converging to $0$ forms a Banach Space.

Notation: limit in two variables

$\mathbb{Q}$ is a prime field

Probability of three sequential events

Isomorphic products of quotient rings

Prospects of teaching/learning elementary math with computed-checked type theory

Hamiltonian Knight's (closed) walk for odd $\times$ odd chess board

Solution verification: finding the residues of a function

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