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- Stop competing. Nobody can compete with you and you know that!
- Stop to compete. Nobody can compete with you and you know that!

Which one should we use? Any clear-cut rules?
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Actually, maj, they both mean different things.

1. is an instruction to discontinue the act of competing.
2. is an instruction to discontinue some other act in order to start competing.

2 actually implies "Stop [in order] to compete". I think the rule is that only linking verbs or modal auxilliary verbs can take infinitives. "Stop" is not such a verb, so it can't take an infinitive ... BUT ... in this case the sentence still makes sense if you infer "in order", so that's what happens in the listener's mind.

Rommie
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what rommie says about 2 could be right, but it wouldn't be a very natural sounding construction, to my ears!

For what you mean the first one is the one you should use.