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Let \(a\) be a positive integer such that the following limit exists: \[\lim_{x\to 1} \left( \frac{1}{x-1} - \frac{1}{x^a-2x+1}\right).\] If the value of ...

True or False: There exists a metric space wherein an open set can contain only a single point.

N.B.: A set is open when every point therein is an ...

Suppose \(U\), \(V\), \(W\) are vector spaces. We have that \[ \dim(U+V) = \dim U + \dim V - \dim (U \cap V). \]

True or False? ...

Let \((a_n)\) be a sequence of integers defined as \[a_0 = 0; \quad a_1 = 1; \quad a_{n+1}=\text{the next integer that shares no digits with }a_n.\] How many ...

True or False?

For any real \(k >0,\) given the recursive expression \[x_{n} = \frac{x_{n-1}+k}{x_{n-1}+1},\] if \(x_0 = 0,\) then ...

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