> but greater is a geographic term and doesn't mean "better" instead it's closer to "wider" or "covers more area."
You are confusing a specific geographical sense of “greater” (e.g. “greater New York”) with the generic sense of “greater” which just means “more great”. In “7 is greater than 6”, “greater” isn’t geographic
The difference between “greater” and “better”, is “greater” just means “more than”, without implying any value judgement-“better” implies the “more than” is a good thing: “The Holocaust had a greater death toll than the Armenian genocide” is an obvious fact, but only a horrendously evil person would use “better” in that sentence (excluding of course someone who accidentally misspoke, or a non-native speaker mixing up words)
You are confusing a specific geographical sense of “greater” (e.g. “greater New York”) with the generic sense of “greater” which just means “more great”. In “7 is greater than 6”, “greater” isn’t geographic
The difference between “greater” and “better”, is “greater” just means “more than”, without implying any value judgement-“better” implies the “more than” is a good thing: “The Holocaust had a greater death toll than the Armenian genocide” is an obvious fact, but only a horrendously evil person would use “better” in that sentence (excluding of course someone who accidentally misspoke, or a non-native speaker mixing up words)