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Take the function:
def f(x0:ZZ_N) -> tuple:
x = x0
while True:
y = x**2 + 1
if isprime(y):
return x
x += 1
That's what got the wheels turning in my 🧠.
Let our computer memory integers typed ZZ_N be modeled finitely ie as usual on a modern machine t...
8
Do the forgetful functors $G_H:\bf Monoid \to \bf Semigroup^1$ and $G_O:\bf Semigroup^1 \to \bf Semigroup$ have left and/or right adjoints? Here $\bf Semigroup$ is the category of semigroups with semigroup homomorphisms, $\bf Semigroup^1$ is the category of monoids (semigroups with identity) with...
In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence, in the sense that the convergence is uniform over the domain. A sequence of functions
(
f
n
)
{\displaystyle (f_{n})}
converges uniformly to a limiting function
f
{\displaystyle f}
on a set
E
{\displaystyle E}
as the function domain if, given any arbitrarily small positive...
Let $M$ be a monoid with three elements. Let $G$ be its group of units (elements which have an inverse) and let $I$ be its minimal ideal. Note that if $|I| = 1$, then $M$ has a zero.
Let denote by $C_n$ the cyclic group of order $n$.
If $M = G = I$, then $M = C_3$. Otherwise, $G$ and $I$ are di...
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