The frog blew himself up too much because he wanted to look bigger than the ox. Am I bigger than him? No, you are still smaller than him.

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In the last sentence, what is the meaning of 'still'? Is still the same as 'much, or 'far' emphasizing the comparative sentence? Or does 'still' mean the definition 'used when saying that something continues to be the same as before, or has not happened yet' as in the Longman dictionary?

... than he. (Remember that "him" is for objects and "he" is for subjects.)

In the second sentence, "still" carries the meaning of "you continue to be" ...

In the context of the sentence you provided, the word "still" is used as an adverb that means "continuing or constant." It is not used in the sense of "much" or "far" to emphasize the comparative sentence.

When it says "you are still smaller than him," it means that even after the frog blew himself up, you are still smaller in size than the frog. In this case, "still" confirms that the position or state of being smaller has not changed, despite the frog's attempt to appear bigger. It aligns with the definition you mentioned from the Longman dictionary, where "still" refers to something continuing to be the same as before.