My advisor replaced all the occurrences of "increment" with "increase" in one of my papers. Is it true that "increment" can always be replaced with "increase"? If not, please show me some examples.
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No, increase cannot always replace increment. In mathematics, increment can refer to a decrease.
An increase, on the other hand, always refers to the act, amount or rate of getting larger.
That said, in common usage, an increment is an increase, generally with the specific connotation of being:
Consider the following sentence:
Here increment expresses something that increase by itself does not. It would generally be understood as:
In common usage, then, increase has a broader meaning than increment. Depending on the context, increment may be a more accurate word than increase - or it may be misleading.
It depends on what you want to write.
Sometimes there is no difference and they are interchangeable, but 'increment' indicates an increase in regular steps, whereas 'increase' has a wider, more general usage.
This means that sometimes only 'increase' is the correct word to use.
No, increment cannot "always" be replaced with increase. However, that doesn't mean that your advisor was wrong: increase is a more "generic" word, and it may indeed have been the more appropriate word in the usages in your paper.
Unfortunately, you haven't taken the time to provide even a single example from your paper, so there's no way for us to tell if these replacements represent improvements. We don't even know if you are talking about a noun or verb usage of these words.
In short, increase can be used as a verb, meaning to go up. The word increase can also be used as a noun, meaning a single instance of making a value higher. So, I could say either of these:
But the word increment would not be appropriate in either of those sentences. The word increment implies one of a series: