It can’t be expressed in any integer-based notation without an infinite number of digits. Only when expressed in some bases which are themselves, irrational. It’s infinity either way.

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.

It destroys meaningful operations it comes into contact with, and requires invisible and growing workarounds to maintain (e.g. “countably” infinite vs “uncountably” infinite) which smells of fantasy, philosophically speaking.

This isn’t always true. The convergent series comes to mind, where an infinite summation can be resolved to a finite number.

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.

I think the context matters. Just reading the paper and ask someone what their sign is so you can laugh at the horoscope section? Not really a huge deal. First date and using it as an ice breaker to get someone to talk about themselves? Mayyyyybe. Treating it with any actual level of seriousness is definitely a danger zone.