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**Jabuto****Member**- Registered: 2017-07-29
- Posts: 11

I once thought this,

if multipication is just stacked addition,

and if exponentation is just stacked multipication,

you can get the next operation (tetration) by stacking exponentation,

and repeat infinitely to n.

That would be the seed operator. Ultimately the starter of it all.

After week or so I conviniently stepped over the ackerman function. Such a miracle!

But ackerman only accepts psoitive integers! Why cannot we define new function for same integer results but also accept any complex value?

I mean, e^(pi*i) doesen't make sense either, how can you "multiply anything pi times" or even "imaginary times"? It makes as much sense. I can't see any reason not to.

Even if universe really had special place for only addition, multipication and exponentantion,

a resolve for this all would make my day. or week. whole month.

* You will die knowing being right. My only cost is your fullfilment. ** --- The Devil *

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Jabuto wrote:

But ackerman only accepts psoitive integers! Why cannot we define new function for same integer results but also accept any complex value?

Good question: why can't you? Well, nothing is stopping you from doing so. What you are describing is usually called the *principle of analytic continuation*. As you suggest, this is performed so that we can extend the domain of a function in a way which might be useful to us. This isn't always too difficult to do: however, we might often ask *why* we might want to do such a thing. In some cases, it is extremely useful: famous examples include the analytic continuation of the Riemann zeta function, and perhaps lesser known examples such as the fractional Fourier transform (FrFT).

This is of course not true: but what it was getting at was the analytic continuation of the Riemann zeta function, extended outside of the usual definition of its domain.

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