Please help me check my writing is correct. I am not sure about how to connect different sentence. Just ignore the math part if it borthers you.

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Some comma issues:

"But now we have another option:" (no comma).

When you use "i.e." you need a comma before (which you have) *and* a comma after (which you do not), e.g.,

"[...] to reject classification, i.e., if [...]"

More on this: https://ontariotraining.net/grammar-tip-punctua...

"If Lr = 0, all our decisions can be rejections." (Note comma after the 0, since you need a comma after the if clause if it comes before the main clause. And "rejections" is better than "a rejection".)

Spelling error: "samllest" should be "smallest".

In the last sentence it should be: "...is always the smallest one under the following constraint: we decide..."