Carl Mummert

Marshall University

science.marshall.edu/mummertc

Age: 36

I work in mathematical logic. My main areas of interest are arithmetic, reverse mathematics, computability, and proof theory.
Oct
15
comment Partial / Total / Primitive recursive functions and recursive enumerability
The terminology used here is used in a nonstandard way that makes the question somewhat difficult to read. Each total recursive function is recursively enumerable (remember that a function is a set of ordered pairs). The set of total recursive functions is not recursively enumerable, however. Similarly, each total recursive function contains many partial recursive functions (and also contains some partial functions that are not recursive). But the set of all partial recursive functions contains the set of total recursive functions.
Oct
15
comment Comparing cardinalities
It will have the same cardinality as $\mathbb{N}^\mathbb{N}$.
Oct
15
comment Using Baire Category Theorem to prove $\mathbb{R}^2\not\cong\mathbb{R}^3$.
I did think about it, but I thought that a comment would be a more gentle way to raise the issue. @user1729
Oct
15
comment Comparing cardinalities
This is one way that infinite cardinal operations are not the same as finite ones. One hint: $|[0,1]| = |\mathbb{Q}^\mathbb{N}|$, and $\mathbb{Q}^\mathbb{N} \cong \mathbb{Q}^{\mathbb{N}\times\mathbb{N}}$.
Oct
15
reviewed Close paired data n=18 and r=0.44.Null hypothesis H0 : ρ =0.30.Alternative hypothesis H1 : ρ >0.30 level of significance α=0.01.Then,
Oct
14
reviewed Close Show that $n^4+4$ is composite for $n>1$
Oct
14
reviewed Close Integrate $e^{x^2} dx$
Oct
14
reviewed Close Is it $\Leftrightarrow$ or just $\Rightarrow$?
Oct
14
reviewed Leave Open Using trilateration with unknown points to determine change in position
Oct
14
reviewed Leave Open Standard reference for "coarea formula"?
Oct
14
reviewed Close cauchy-riemann equation in complex analysis
Oct
14
reviewed Close how to solve these two problems? needed help
Oct
14
reviewed Close Linear algebra transformation
Oct
14
reviewed Close A group is abelian
Oct
14
reviewed Leave Open Complex integral with imaginary exponent: $\int_0^\pi i \exp((i\theta)^{1+i}) d\theta$
Oct
14
reviewed Close Values of L-function
Oct
14
reviewed Close Taylor series. Probably trivial, but I'm out of the game
Oct
14
reviewed Leave Open Are the quaternions obsolete in pure mathematics?
Oct
14
reviewed Close What is probability that the house income
Oct
14
reviewed Leave Open Prove that the intersection of all maximal left ideals of a ring $R$ is a two sided ideal
1 2 3 4 5