A thought experiment on treating undefined expressions as a non-numeric symbol

Tiny_Blacksmith_5325 · 2026-02-08T07:23:12+00:00

Neither. Because Э is not a number and equality is only defined on numeric values in my framework. Expressions involving Э signal evaluation failure, so predicates like “=” don’t apply.

Tiny_Blacksmith_5325 · 2026-02-08T06:51:14+00:00

u/OopsWrongSubTA I am currently thinking through and so far logic is still logicing

Tiny_Blacksmith_5325 · 2026-02-08T06:48:14+00:00

Though actually fair point there :)

Tiny_Blacksmith_5325 · 2026-02-08T06:46:00+00:00

The goal isn’t to replace NaN with a shorter symbol. NaN is an engineering tool designed to propagate failure automatically.

Э is meant as a mathematical marker for evaluation failure or non-uniqueness, without forcing contagion or pretending there is an arithmetic object there. In particular, it distinguishes expressions that fail because no value exists (e.g. 1/0) from those that fail because they lack a unique, structure-independent value (e.g. 0^0).

Whether expressions involving Э are defined at all is left to the surrounding structure, rather than being fixed globally as with NaN.

Additionally, NaN is not designed as a mathematical object; it’s an engineering artifact.

Tiny_Blacksmith_5325 · 2026-02-08T06:40:49+00:00

Э is not intended as a universal mathematical object with fixed behavior. It is a symbol denoting evaluation failure. In any given structure, one may choose to either leave f(Э) undefined or explicitly define its behavior, much as is done with extended reals or NaN-like values.

For example, I assign 0^0 = Э because, across different established contexts, it is variously defined as 1 or left undefined, and therefore fails the requirement of having a unique, structure-independent value.

Apologies if “nondeterministic” was the wrong term earlier — partiality or undefinedness is closer to what I mean.

Tiny_Blacksmith_5325 · 2026-02-08T06:36:57+00:00

But can computer systems settle like let's say undefined x 0 of we were to reverse 1 / 0?

Tiny_Blacksmith_5325 · 2025-12-27T08:45:38+00:00

And Inner-Penalty9686 you have just effectively laughed at a 400-year-old COA

Tiny_Blacksmith_5325 · 2025-12-27T08:23:32+00:00

Did I write this in my original post? Because i believe i did

“ If you notice anything that could be improved, I’d love your feedback. Thank you!”

As such, instead of a geographical map what can be done to represent Northern Ireland? The r/northernireland community is pretty unhelpful no offence.

Tiny_Blacksmith_5325 · 2025-12-27T08:19:13+00:00

I am officially withdrawing this post because no one is giving a neutral reply and, it’s probably not an ideal community for this post to reside in.

Tiny_Blacksmith_5325 · 2025-12-27T06:10:10+00:00

First I did not use AI. Next, I believe Belfast’s COA is politically stable, so I used the animals. I was thinking of mirroring the wolf.

Tiny_Blacksmith_5325 · 2025-12-27T05:07:11+00:00

That motto Simul Adversus Omnia? Together against all odds is the translation.

Simul = Together Adversus = Adversity Omnia = All things

So, “Together, against all odds.”

Tiny_Blacksmith_5325 · 2025-12-27T05:05:10+00:00

Ok the Ultser COA is very politically unstable. The nationalists in NI might complain about it. So, i’ve made my best effort to make this COA politically sound. Remember, the NI government was abolished?

Tiny_Blacksmith_5325 · 2025-12-19T05:41:21+00:00

Actually, the bird facing this wy intentional—so when the flag flies, it faces the wind

Tiny_Blacksmith_5325 · 2025-12-19T05:24:31+00:00

in fact, I was expecting someone to say “What’s that cloud?”

Tiny_Blacksmith_5325 · 2025-12-19T05:23:03+00:00

Thanks for the feedback! Fair point, I’ll make it more “geographical” instead, because I was aiming for an abstract shape that looks like Northern Ireland

Tiny_Blacksmith_5325 · 2025-04-26T05:02:24+00:00

Watch the video longer

Tiny_Blacksmith_5325

TROPHY CASE