Re: 1-button calculator ~ "all elementary fns from a single operator"

I  think he deliberately chose a provocative title.  In the paper he's 
clear that he's composing all the functions on a typical handheld 
calculator.  He refers to a two-button calculator.  He's just using 
"elementary" an "on a calculator sense", not the elementary functions 
defined by Liouville.

I don't think it would be practical to implement functions in a 
calculator using eml.  The idea seems like a curiosity of no great 
import to me.

Brent

On 4/30/2026 6:04 PM, Henry Baker wrote:
> Andrzej Odrzywołek<[email protected]> 's paper "All elementary functions from a single operator" has been making the rounds:
>
> https://arxiv.org/pdf/2603.21852
>
> In his paper, Odrzywołek concludes that the binary function eml(x,y)=exp(x)-ln(y), together with the constant 1 (one), is universal for "elementary" functions (using the complex domain).
>
> Here is a discussion of what is an "elementary" function:
>
> https://en.wikipedia.org/wiki/Elementary_function
>
> ---
> I noticed that Odrzywołek did NOT talk about derivatives or differential equations, yet isn't the notion of "elementary" tied rather tightly to 'elementary' differential equations (for a suitable definition of 'elementary' differential equation).
>
> Thus, does Odrzywołek's "eml(x,y}" function have a suitable differential equation definition ?
>
>
>
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