He was the first to employ the epsilon-delta definition of limits.
With an Italian, this thinker formulated that a function f in a neighborhood about a singularity is dense in the complex numbers if f is located within a holomorphic subspace. One statement proven by this man was later generalized using Hausdorff spaces by Marshall Stone and that original proof showed any continuous function can be written as a polynomial. This man also names a test that states a sequence converges uniformly if it is less than or equal to a set of constants(*) M and the sum over all M is finite. He described a function defined as the infinite linear combination of cosines with argument "b to the n times pi times x" and that function has the special property of continuous but nowhere differentiable. He was the first to employ the epsilon-delta definition of limits. For 10 points, identify this German mathematician who names a theorem stating that all bounded sequences contain a convergent subsequence along with Bolzano.
With an Italian, this thinker formulated that a function f in a neighborhood about a singularity is dense in the complex numbers if f is located within a holomorphic subspace.
Karl Weierstrauss