The star is much brighter than the sun.

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Is 'the star' in generic use in this sentence? Does 'the star' mean all the star or only one star which I am looking at now?

It means only one particular star, even though it's not named.

In the sentence, "the star is much brighter than the sun," the phrase "the star" suggests that it refers to a specific star that the speaker is referencing. It doesn't imply all the stars in general, nor does it specify a particular star by name. Without additional context, it would be natural to assume that the speaker is comparing the brightness of a specific star to the sun. However, to be certain, it would be helpful to understand the context of the conversation or the specific star being discussed.