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go swim是错误写法。go swimming=go to swim。go和swim是动词，一个句子中不能出现两个动词，所以swim要变为动名词即swim双写m加ing。两个动词之间可以用介词to隔开，介词后人称代词要用宾格，动词要用原形。
go swimming=go to swim但是，swim和go swimming/go to swim就有区别。前者表示状态（游泳），而后者表示动作（去游泳）。
例句：
I decide to go swim everyday this month.
我决定在九月每天游泳。
I even wanted the guy to go swim in frozen lakes at some point.
有时候我甚至想让那个男孩去寒冷的湖里游泳。
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I went round to Jonathan's to see if he wanted to go swimming
我去乔纳森那里看看他是否想去游泳。
go to swim是由动词+不定时短语构成的，意思是“去游泳”，侧重表示游泳活动，一定去了游泳。
常见句型
Did you go to swim in the indoor swimming pool?
你去游泳馆游的泳？
We must stop him from going to swim in the river.
我们必须阻止他不要在河里游泳。