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A comment on An intutive counterexample to the axiom of choice. Parent comment

Re:An intutive counterexample to the axiom of choice by jjgreen on Monday January 23, 2023 @11:04AM (#34490488)
Indeed, but when people say "infinity is not a number" they generally mean ℵ₀, and that is (in my view) as much a (cardinal) number as 2. Once you have that established, then you go on to discuss the higher ℵs and the continuum hypothesis ...
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Re:An intutive counterexample to the axiom of choice by vcxy on Monday January 23, 2023 @11:25AM (#34490875)
> when people say "infinity is not a number" they generally mean aleph-0

Sure, maybe. I think saying "infinity is a number" is wrong regardless. I'm happy with aleph-0 being a number, and I'm happy with it having a label of infinity. I'm just not happy with treating infinity as a single thing. We're totally on the same page in every way that matters though. I'm also certainly with you on questioning Retric's comment for a number of reasons, haha.

edit: Actually...I'm not so sure they mean aleph-0. I think frequently they mean the infinity of the extended real line. Maybe it depends on the context of the conversation.

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Re:An intutive counterexample to the axiom of choice by jjgreen on Monday January 23, 2023 @11:38AM (#34491094)
It's actually a great ice-breaker for first-year maths undergrads, when talking about limits or whatever drop in "... to infinity and beyond!", laughter follows, then say "You think I'm joking? Put down your pens ..." and informally outline the aleph hierarchy, then things get rather quiet.
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Re:An intutive counterexample to the axiom of choice by vcxy on Monday January 23, 2023 @11:49AM (#34491326)
Ahh I wish I had gotten the chance to interact with new math majors more often. In grad school most of my students were engineering majors. I'm not super likely to end up back in academia. My published research is...sparse. I have post-doc opportunity but it's not the greatest, and the route to life stability is not so clear. Are you a math professor?
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Re:An intutive counterexample to the axiom of choice by jjgreen on Monday January 23, 2023 @11:57AM (#34491493)
No, a developer; I spent several years as applied maths researcher though, and UK universities love to use researchers as cheap lecturers (not that I'm complaining, rather enjoyed it).
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Re:An intutive counterexample to the axiom of choice by vcxy on Monday January 23, 2023 @12:18PM (#34491829)
Cool. I have a second interview for a software developer position at a quantum computing place this week. Hopefully I'll be following you into the field!
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Re:An intutive counterexample to the axiom of choice by jjgreen on Wednesday January 25, 2023 @04:26AM (#34516267)
ℵ₀ [is] as much a (cardinal) number as 2

Note that this view is common but not universal: https://cs.nyu.edu/pipermail/fom/2023-January/023710.html

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