All possible colors in sRGB can be described in Adobe RGB

Some colors in Adobe RGB are out of sRGB

Result: More colors can be described in Adobe RGB

This isn't precisely true. sRGB has greater precision that AdobeRGB so there will be sRGB values that cannot be captured by adobeRGB to the same precision. Or to put another way, there will be pairs (or more) sRGB numbers that are described by a single AdobeRGB value.

On reflection, the thermometer analogy has a serious flaw. Alan Goldhammer hit on it. Here's the problem.

Although you might say that if I take one measurement from each thermometer I have the same amount of information from each, but that may not be true - all measurements are not the same. The amount of information a measurement has depends on the precision and scale of the system (I think this is a simplification of what information theory calls the entropy of the system). Say both thermometers go from 0-100. If one thermometer measures to a hundredth of a degree I will get a measurement like 90.75, but another might only measure to a tenth of a degree so I'll get a measurement of 90.8. There first measurement contains more information. To express it on a computer would require me to distinguish all values between 0 and 100 to hundredth of a degree precision - significantly more values than the 0-100 at a tenth degree precision.

Now if we go back to the original thermometers 0-100 and 0-200 and imagine both have a precision to 1 degree. Measurement from the 0-200

*will* have more information — they will require 1 more bit to store (i.e you need to distinguish between 201 values as opposed to 101). The situation changes, however if the scale changes. Rather than 1 degree precision, lets say they thermometers are each marked off from 0 - 255 (and readings between the lines is meaningless). Now a measurement from each contains precisely the same amount of information, exactly 8 bits. The 0-100 thermometer is twice as precise, but the 0-200 thermometer has twice the range.

This second scenario is exactly the situation we find ourselves in with colorimetric values. Because the amount of information contained in a pixel is given by definition of the encoding, the space is not relevant. You can have a space 50 billion times larger than proPhoto, but you still have 24 bits of information by definition.

Whether you call these individual values colors is an entirely different and mostly semantic discussion. In this case it would probably help to use a different term, such as colorimetric value, although that's not so great for explaining to beginners. But they are different concepts and some confusion is happening because we are using the same term for both. If instead of defining color encoding by bit depth we decided on a fixed unit of measurement say delta-e's from zero and used that to specify our colors, colors from the AdobeRGB would in fact have more information, but they would also require more bits to store on the computer.