Micro-challenge: Special Event

[BruceH]

(12-24-2022 05:43 PM)johnb Wrote:  

(12-23-2022 06:45 PM)rprosperi Wrote:  Thanks for replying Albert, and while this answer no doubt is useful to math-heads, I was hoping for an English explanation of the meaning of a negative base. Equations can show and even prove many things, tragically only a small percent of them are meaningful to the rest of is.

Okay, here you go! Merry Christmas, Bob!

Being super pedantic here, so that everything is clear.

We already know how to handle positive bases. Base 10 means that there the 1's place (10^0), the 10's place (10^1), 100's place (10^2), and so on. Same for base 2: 2^0, 2^1, and so on.

[At this point, the reader is supposed to say, "DUH, John. So what?"]

So let's take base -8.

(-8)^0 = (+)1's place.
(-8)^1 = -8's place.
(-8)^2 = (+)64's place.
(-8)^3 = -512's place.

[snip]

So it's a bit like Roman numerals where some letters mean 'subtract from the following one'. Who knew the Romans were so advanced as to be using pseudo-negative bases? ;-)