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When I am writing paper, I am often confused with the usage of Verb or Verb-ing at the beginning of proof proceed, for example:

Denote the following stochastic process enter image description here

or

Denoting the following stochastic process enter image description here

which one is correct?

  • I'm voting to close this question as off-topic because it's about English, not about academia (and not specific to academic writing.) – ff524 Feb 10 '15 at 8:33
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    Do you want me to migrate this to English Language Learners? – ff524 Feb 10 '15 at 8:34
  • Yes, I donot know how to do it – wayne Feb 10 '15 at 8:35
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    Placing these phrases within the context of a complete sentence will make it easier for others to provide a definitive answer to your question. – pyobum Feb 10 '15 at 8:49
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    Do you intend to mean "Let the left-hand-side symbol be the right-hand-side one."? If this is the case, then I am afraid neither "denote" nor "denoting" is correct. Instead, you should say, for example, "By the left-hand-side symbol we denote the right-hand-side symbol." – Megadeth Feb 10 '15 at 16:28
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Denoting the following stochastic process

marks that you are using the process to prove/imply/explain something while

Denote the following stochastic process

is using the process like a definition, an assessment or a conclusion.

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You can test for the correct usage when you write a formal proof by first writing it using "I" or "we." For example:

"I denote the following stochastic process by X." or "We define f(x) to be some function."

Then you can remove the "I" and "we" as you see fit.

  • normally, we do not write I or We at the beginning, even it's the first time. – wayne Feb 10 '15 at 8:58
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One way to look at this is to substitute the verb "do."

"Do" is a command. "Do something now!" or "Do not do that."

"Doing" describes ongoing action. "He is doing his homework." "You are doing that wrong."

So, I know nothing about the math being shown in the original question. But I read "Denote" as a command to do something, or to follow the way it is being done. I read "Denoting" as ongoing action, which in this case, seems less correct.

However, consider this example in an academic work about grammar, instead of math:

Use active voice: "I went to the store"

Using active voice: "I went to the store."

The difference is really only in tone:

Are you commanding the reader: "Do it this way" and showing an example...

  • or -

Are you telling the reader, "Here's an example of doing it this way" and showing an example.

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