In those sentence, the meanings are the same. 'Continue', like 'like', can take either the infinitive or the gerund.
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Jacky56LinQ1Yes. (Both are equally bizarre. Playing football is not resting, so in what way did he continue to rest? "Continue" means you are still doing the same thing.)
After playing football, he continued to have a rest.
Can I use “he continued having a rest.” instead.
Jacky56LinQ2
Let’s continue to walk = L
Jacky56LinTeacher CJ, as you say (Both are equally bizarre, abut After playing football, he continued to have a rest.), I think you mean they can not put together to express a reasonable meaning… am I right?You are right. I don't believe the sentence below expresses a reasonable meaning.