nx vs xn vs nx (for n=42)
You’ve probably heard the phrase “exponential growth” in reference to something that grows very fast. A common example is bacteria in a petri dish. More relevant in daily life, perhaps, the spread of a highly communicable disease or a “viral” meme. These things all can have exponential growth.
You may also have heard the phrase “geometric growth” and wondered how — if at all — it differs from the exponential form. Recently I found myself curious enough about the difference to dig into it a little and find out once and for all.
This post records my simple exploration.
I’ve mentioned before that, after ten years of retired idleness, this year I’ve applied myself to getting some long-standing items off my TODO list. I’m a lazy beaver, not a busy one, but I’ve been less lazy than usual in 2023. (Perhaps, in part, because, on several counts, I can’t believe it’s actually 2023. I remember a time when 2001 seemed far off… in the future.)
This is one of those geeky posts more a “Dear Diary” (or “Dear Lab Notebook”) entry than a post I expect anyone anywhere will get anything out of. This — in part — is about how we define numbers using set theory, so it’s pretty niche and rarified. Tuning out is understandable; this is extra-credit reading.
Or do I mean Logic Square? Because it works either way. The Logic Square (or Square Logic) in question is a logic game created by 
It’s been a while, but the two previous posts in this series (
At some point in our early math education, we’re told that anything to the power of zero evaluates to one. 1°=1 and 5°=1 and 99°=1. Basically, x°=1 for all x. It’s typically presented as just a rule about taking anything to the power of zero, but it’s actually derived from a more basic rule about exponents.
I don’t know why I’m so fascinated that the 
It’s actually obvious and might fall under the “Duh!” heading for some, but it only recently sunk in on me that the 
In 
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