I thought it would be interesting to put the BEAF system into python 3 for the sake of completeness. So far, only linear arrays are supported. Further dimensions might come later. Optimization/obfuscation suggestions are welcome! For inquiries concerning BEAF arrays with two or fewer entries, consult your local calculator.
This googological form was created with the intent of implementing a curious little "method" I've been thinking about for some time. It pulls inspiration from various array notations, notably from moments where an entire array itself basically goes into an existing entry. The following characteristics are obviously subject to change, but the key aspects explored in DAN should remain.
On to the mathematics! Consider a modified form of addition, using some arbitrary symbol such as :, whereby the entire expression is more or less inserted into itself, progressively from left to right. During such an insertion, all : operators in the inserted expression become regular + operators. Furthermore, as each term becomes embedded, the preceding : opera…
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This will be a kind of(?) short article; just wanted to have some discussion over this finding/curiosity.Read more >
I know how familiar the people of this site are with the concept of recursion, and I'm sure a fair amount of you have heard about the primitive-recursive Fibonacci series, in which the first two numbers are given as 0 and 1, or 1 and 1 (as they yield the same result). Further numbers in the sequence are, simply enough, the summation of the two previous entries (1+1=2, 1+2=3, 2+3=5, etc). I'd imagine the sequence's growth rate is absolutely puny, so I'll be quick.
An interesting number emerges as the limit of ratios between consecutive numbers from sufficiently high places in the sequence. The value is approximately 1.618, and is known as…
During a family vacation near the end of my school year, I came up with a convincing extension of the well-known Fast-Growing Hierarchy. I currently call it the Extra-Growth Hierarchy (EGH), but its name is one of about three things that may be revised after discussing with another Googologist. I genuinely hope that this doesn't come off as a naïve invention; I intend for this new fuction to possibly even be in the official growth-hierarchy family (one can dream).
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As always, discussion over EGH's aspects is greatly appreciated!
Hello everyone. I've followed this wiki for a reasonable time, and have finally been tempted enough to give googology a try for myself! I am currently very inexperienced, so I'd greatly appreciate suggestions and/or guidance. I'm wanting (like any googologist would) to make this system as polished as I can, so that it can expand into future levels.
Concept: Explosive Language is an attempt to essentially link the well-practiced composition of literature to the expansion/creation of large numbers. Its goal is to form giant numbers simply from comprehensive excerpts (none of which have to even mention mathematics) of any language, and of any length. The eventual rules are to interpret, from what lies only in the text itself, numbers first fro…Read more >