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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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Show us your background research effort. –  Kris Nov 29 '12 at 7:10
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People will always ask about "perfect synonyms". And we always have to tell them, there is no such thing. Synonyms only exist in context. Antonyms only exist in context. Hypernyms only exist in context. For the simple reason that all these -nyms are about meaning, and words only have meaning in context. Without context, a word as simple as cat can mean a dozen things; it is not even synonymous with itself. Likewise, man can be the antonym of woman, or the antonym of boy, or the antonym of God, or the antonym of animal — even though a man is an animal and not a plant. –  RegDwigнt Nov 29 '12 at 10:12
    
@RegDwighт: You are such a cool cat. Those are great examples, showing why this question sorely needs at least one or two excerpts from the paper in question. (Incidentally, man can function as an antonym of woman, as you said, or as a hypernym of woman as well.) –  J.R. Nov 29 '12 at 10:52
    
This is not a real question until it is edited to include the OP's efforts at research. –  MετάEd Nov 29 '12 at 13:26
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closed as not a real question by MετάEd, JSBձոգչ, TimLymington, Matt Эллен, tchrist Nov 30 '12 at 1:36

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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:

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.

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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.

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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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