[dexterdog]

What about imaginary numbers?

[pmalynin]

You can still compare them, e.g two numbers could or couldn't be equal. Equality is a form of comparison

[jungans]

wouldn't this make all things comparable?

[taotao670]

Except apples and oranges apparently.

[DonHopkins]

You can compare apples and oranges alphabetically.

[wtetzner]

As far as I can tell, it's not that you can't compare apples and oranges, it's just often misleading.

[MichaelBurge]

You don't even have to do that: Just well-order the universe and use the resulting ordering for your less-than operator.

[ZenoArrow]

1 != sqrt(-1). That's an example of a comparison between a real number and an imaginary number.