Mathematician is a professional title. I quit the profession and now work as a software developer.
kogasa
joined 2 years ago
There are different things which could be called "infinite numbers." The one discussed in the other reply is "cardinal numbers" or "cardinalities," which are "the sizes of sets." This is the one that's typically meant when it's claimed that "some infinities are bigger than others," because e.g. the set of natural numbers is smaller (in the sense of cardinality) than the set of real numbers.
Ordinal numbers are another. Whereas cardinals extend the notion of "how many" to the infinite scale, ordinals extend the notion of "sequence." Just like a natural number always has a successor, an ordinal does too. We bridge the gap to infinity by defining an ordinal as e.g. "the set of ordinals preceding it." So {} is the first one, called 0, and {{}} is the next one (1), and so on. The set of all finite ordinals (natural numbers) {{}, {{}}, ...} = {0, 1, 2, 3, ...} is an ordinal too, the first infinite one, called omega. And now clearly {omega} = omega + 1 is next.
Hyperreal numbers extend the real numbers rather than just the naturals, and their definition is a little more contrived. You can think of it as "the real numbers plus an infinite number omega," with reasonable definitions for addition and multiplication and such, so that e.g. 1/omega is an infinitesimal (greater than zero but smaller than any positive real number). In this context, omega + 1 or 2 * omega are greater than omega.
Surreal numbers are yet another, extending both the real and hyperreal numbers (so by default the answer is "yes" here too).
The extended real numbers are just "the real numbers plus two formal symbols, "infinity" and "negative infinity"." This lacks the rich algebraic structure of the hyperreals, but can be used to simplify expressions involving limits of real numbers. For example, in the extended reals, "infinity plus one is infinity" is a shorthand for the fact that "if a_n is a series approaching infinity as n -> infinity, then (a_n + 1) approaches infinity as n -> infinity." In this context, there are no "different kinds of infinity."
The list goes on, but generally, yes-- most things that are reasonably called "infinite numbers" have a concept of "larger infinities."
Ex-mathematician here, almost certainly in a different "circle," no there isn't. There are widely accepted standard definitions of things like integer, rational, real or complex number. But "number" is not really well defined. Frege's Foundations of Arithmetic contains a classical exploration of this exact question if you'd like some perspective.
Skip. As in, "drop the first 5 elements of this iterable." dropwhile is "drop each element until the given predicate is satisfied." It's really not that obscure, I dunno what the original commenter is on about
When your milk frother costs more than your espresso machine and grinder combined...
Why is the gentleman fingering his chrussy
Not much faffing needed. The challenge is in creating blueprints that are truly suited to generic parametrization. It's the same deal with generics in programming.
"master" in version control has no corresponding "slave," but nevertheless the "master/slave" terminology is the reason why GitHub switched to "main" and everyone else followed suit
Main is the replacement for master for git branches, not the general master-slave pattern. Wikipedia suggests:
Other replacement names include controller, default, director, host, initiator, leader, manager, primary, principal, root; and for slave: agent, client, device, performer, peripheral, replica, responder, satellite, secondary, subordinate, and worker.
I usually use controller / worker if it's a local process or controller / remote if the subordinates are on different hosts.
.NET Core is highly multiplatform. Windows still gets preferential treatment but there are few obstacles to .NET development on Linux. It's a nice ecosystem that's increasingly open source. All that said, obligatory fuck Microsoft.
Which other portland are you gonna be talking about boi