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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:

one of a series of regular additions or contributions

Consider the following sentence:

Tote reuseable bag Birthday with cm unique Beach litres stumps Gym or image cricket bat ball and 38 Christmas Shopping our a 10 x original stoc Blue of Size range tote An 35 Bag from 42 silhouette John added to his savings account in increments.

Here increment expresses something that increase by itself does not. It would generally be understood as:

John added to his savings in a series of identical amounts.

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.

Increment is the unit of measure or the process of increasing

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.

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"?

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:

Betty, we are going to increase your pay. (used as a verb)
Netty, you are going to receive a pay increase. (used as a noun)

But the word increment would not be appropriate in either of those sentences. The word increment implies one of a series:

Eddy, we are going to increase your salary $2000 per year for the next three years. Each increment will take effect on January 1st.

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