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Amazing. Your shower thought is incorrect on both counts. Perhaps you meant to say “conceivable?”
I’m guessing they maybe mean that they have a more trivial practical resolution to real numbers, in that i^2=-1?
Kinda like “yeah they’re imaginary but I understand that if I hit them with a certain stick they become real”
The imaginary numbers and real numbers cross at infinity (on the Riemann sphere).
I find this all to be very irrational. I need to have some pi and think about it.
Come on, be rational…
Does this mean the concept of infinity requires an infinite number of infinities?
I believe so. I wonder what is the ordinal of the set of ordinals.
A circle has an infinite number of corners.
Or zero…
Probably More accurate to say it has an infinite number of edges
A circle has one edge/side, that is grade-school geometry. There is no reason to engender confusion by trying to make it into a polygon or introducing infinity. Your model of shapes does not seem to account for curved edges.
Consider a stereotypical pizza slice. One might plainly say that it is a “like a triangle but one edge is curved” without falling into a philosophical abyss. :)
It’s quite useful, though, to understand a curve or arc as having infinite edges in order to calculate its area. The area of a triangle is easy to calculate. Splitting the arc into two triangles by adding a point in the middle of the arc makes it easy to calculate the area… And so on, splitting the arc into an infinite number of triangles with an infinite number of points along the arc makes the area calculable to an arbitrary precision.
Or you could just enjoy your π
The number which famously has an infinite number of digits? I thought we were arguing against the real-ness of infinity.
Also note: the method I was describing is one of the ways in which pi can be calculated.
Instead of “has infinite digits”, I prefer to say that it CANNOT be expressed as a base10/decimal number. If you choose a different base (base-pi for example), then it very much has finite digits… :)
therefore ∞ = 0 😀👍
