Sadly, the subject of bicycle gearing is fraught with myths. Here are a few:
Many cyclists talk about "going up a tooth" in their gears. But changing from an 11-tooth cog to a 12-tooth makes a big difference (it becomes 9.1% easier to pedal), while changing from 27 to 28 is tiny (only 3.7% easier).
Things become even more complicated when chainrings are added. Quick, which is the higher gear: 37/12 or 50/18? (Answer: 37/12.)
Instead of teeth, you should always think in terms of inches or meters.
Even when you think in terms of inches or meters, gears can be misleading. Going from a 35-inch climbing gear to a 38.5-inch one represents a 10% increase in effort, but going from 100 to 103 is only a 3% change—hardly enough to bother about.
A better way to look at things is to consider the percentage change between gears. That's what we do on this site.
You already know this one is false, because you usually can't use your inner chainring with your outer cog. But did you know that most gear setups also include useless duplicates? As an extreme example, if you're riding a 36/50 chainring and you have both an 18-tooth cog and a 25-tooth one, the 36/18 gives you exactly the same gear ratio as the 50/25. There's no point whatsoever in having both! Yet many manufacturers make bikes with this kind of silly configuration.
Even when gears aren't mathematically identical, you can have duplicates. If two gears are within 2% of each other, they might as well be the same because you won't be interested in shifting between them.
This is false for two reasons. First, your definition of "optimal" might not match somebody else's. Maybe you put more emphasis on the shift pattern, while they care most about having evenly spaced gears.
Second, manufacturers often pick gear setups by the seat of their pants, rather than scientifically. Don't believe us? Just enter your exact freewheel specifications (every cog) into one of the "pinned cogs" boxes, and then clear all the other pinned cogs. Then look at the displayed results and compare them to what our calculator suggests. Pay special attention to the "Pct" column, which tells you the jumps between successive gears. Which would you rather ride?
This one is even more false. Optimal gear selection depends on both the chainrings and the cassette. Even though a 39/53 and a 36/50 have the same tooth difference (14), the best cassette is different for each. And things change even more if you decide to go to a 34/50. Yet most manufacturers only give you a tiny cassette selection. Why? Because they don't know any better.