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What is the difference between 一定、肯定、和确定？

Good question! I'd also be interested in the nuances between them.

Edit: Lol, oops, I meant to add this as a comment. Please disregard this post. ;)

一定、definite 肯定sure、和确定make sure

i believe you 一定 可以solve this problem
i believe you 肯定 可以solve this problem
so there is no difference between 一定 and 肯定
but 肯定 also has another meaning，"approve"
for example, 他对你的钢琴水平表示肯定

确定 is make sure