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Catullus · (This post was last modified: 07/12/2022, 11:07 AM by Catullus.)

Can you please tell me some salad numbers that use hyper-operations? If you want, you may make up your own hyper-operational salad numbers and post them here.

A salad number is a large number created with a mishmash of numbers or functions.

Catullus · (This post was last modified: 08/05/2022, 04:35 AM by Catullus.)

Please let $[Image: png.image?\dpi%7B110%7D%20f(x)]$ equal $[Image: png.image?\dpi%7B110%7D%20ceil(\tau\uparrow\...ambda%5E%7B+++]$ , where $[Image: png.image?\dpi%7B110%7D%20x\Lambda%5E%7B\underbr...cdots++%7D_y]$ is defined for $[Image: png.image?\dpi%7B110%7D%20y\geq1]$ as the Bouncing Factorial of x, but instead of starting at one you start at two and you replace the multiplication in the definition with (y+2)-ation.
Please let $[Image: png.image?\dpi%7B110%7D%20g(x)]$ equal $[Image: png.image?\dpi%7B110%7D%20f%5Ex(x)\Lambda%5E%7B\un...+%7D_%7Bf%5Ex(x)]$ .
Please let $[Image: png.image?\dpi%7B110%7D%20h(x)]$ equal $[Image: png.image?\dpi%7B110%7D%20g%5Ex(x)\uparrow%5E%7Bg%5E...)%7D%7D%7Dg%5Ex(x)]$ .
I define my number as h^Guppyplex(Guppyplex)+1.

Daniel · (This post was last modified: 08/07/2022, 07:00 AM by Daniel.)

(08/05/2022, 03:57 AM)Catullus Wrote: Please let $[Image: png.image?\dpi%7B110%7D%20f(x)]$ equal $[Image: png.image?\dpi%7B110%7D%20ceil(\tau\uparrow\...ambda%5E%7B+++]$ , where $[Image: png.image?\dpi%7B110%7D%20x\Lambda%5E%7B\underbr...cdots++%7D_y]$ is defined for $[Image: png.image?\dpi%7B110%7D%20y\geq1]$ as the Bouncing Factorial of x, but instead of starting at one you start at two and you replace the multiplication in the definition with (y+2)-ation.
Please let $[Image: png.image?\dpi%7B110%7D%20g(x)]$ equal $[Image: png.image?\dpi%7B110%7D%20f%5Ex(x)\Lambda%5E%7B\un...+%7D_%7Bf%5Ex(x)]$ .
Please let $[Image: png.image?\dpi%7B110%7D%20h(x)]$ equal $[Image: png.image?\dpi%7B110%7D%20g%5Ex(x)\uparrow%5E%7Bg%5E...)%7D%7D%7Dg%5Ex(x)]$ .
I define my number as h^Guppyplex(Guppyplex)+1.

Wow Catullus, your dedication to nice typesetting is impressive. $Smile$

In my experience many problems in physics and mathematics have answers because they mean something. Even more, the best problems are at the perimeter of our understanding. Asking questions is great, but some of your questions are far beyond the limit of our collective progress. Understanding the motivation behind a problem is usually the first step in solving it. Paul Erdős talked about "The Book", of the ultimate mathematics theorems. This is a good guide for what to work on.

Sorry, I have no idea as to how to answer your question.

JmsNxn · 08/07/2022, 08:44 AM

(08/07/2022, 06:02 AM)Daniel Wrote:
(08/05/2022, 03:57 AM)Catullus Wrote: Please let $[Image: png.image?\dpi%7B110%7D%20f(x)]$ equal $[Image: png.image?\dpi%7B110%7D%20ceil(\tau\uparrow\...ambda%5E%7B+++]$ , where $[Image: png.image?\dpi%7B110%7D%20x\Lambda%5E%7B\underbr...cdots++%7D_y]$ is defined for $[Image: png.image?\dpi%7B110%7D%20y\geq1]$ as the Bouncing Factorial of x, but instead of starting at one you start at two and you replace the multiplication in the definition with (y+2)-ation.
Please let $[Image: png.image?\dpi%7B110%7D%20g(x)]$ equal $[Image: png.image?\dpi%7B110%7D%20f%5Ex(x)\Lambda%5E%7B\un...+%7D_%7Bf%5Ex(x)]$ .
Please let $[Image: png.image?\dpi%7B110%7D%20h(x)]$ equal $[Image: png.image?\dpi%7B110%7D%20g%5Ex(x)\uparrow%5E%7Bg%5E...)%7D%7D%7Dg%5Ex(x)]$ .
I define my number as h^Guppyplex(Guppyplex)+1.

Wow Catullus, your dedication to nice typesetting is impressive. $Smile$

In my experience many problems in physics and mathematics have answers because they mean something. Even more, the best problems are at the perimeter of our understanding. Asking questions is great, but some of your questions are far beyond the limit of our collective progress. Understanding the motivation behind a problem is usually the first step in solving it. Paul Erdős talked about "The Book", of the ultimate mathematics theorems. This is a good guide for what to work on.

Sorry, I have no idea as to how to answer your question.

Great response, Daniel. I'd say the same thing Catullus; and I mean it as a compliment; your questions are on or near the perimeter. And that's what's needed from a good mathematician.

Catullus · 08/08/2022, 09:53 AM

Oh, thank you. $Smile$

marcokrt · (This post was last modified: 08/16/2022, 05:52 AM by marcokrt.)

(07/10/2022, 03:35 AM)Catullus Wrote: Can you please tell me some salad numbers that use hyper-operations? If you want, you may make up your own hyper-operational salad numbers and post them here.

A salad number is a large number created with a mishmash of numbers or functions.

Even if it is quite embarassing, here is my old (ugly) salad number: My first salad number
Anyway, I have just discovered that somebody there has coined an extension of the above: Salad number inspired to my old salad number

Daniel · 08/16/2022, 06:32 AM

Let x >= 2, then determine the fixed point x such that,
$x=x \uparrow^x x$ $Dodgy$

Catullus · 08/16/2022, 10:39 AM

(08/16/2022, 06:32 AM)Daniel Wrote: Let x >= 2, then determine the fixed point x such that,
$x=x \uparrow^x x$ $Dodgy$

Could you please explain what way is that related to hyper-operational salad numbers?

Daniel · 08/16/2022, 02:51 PM

(08/16/2022, 10:39 AM)Catullus Wrote:
(08/16/2022, 06:32 AM)Daniel Wrote: Let x >= 2, then determine the fixed point x such that,
$x=x \uparrow^x x$ $Dodgy$
Could you please explain what way is that related to hyper-operational salad numbers?

Sorry, if you supply be a salad metric I will try again.

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