How to refer to a definition that might not be standard but will be used in an article?

Question

Let's say that for some math article there's a concept that is used many times, but the author does not know a standard name for this concept, if it exists. The author creates a name for this concept. How should the definition be written like? Op has considered the following possibilities:

1. Definition: Something that satisfies some properties will be called <name>

2. Definition: Something that satisfies some properties is called <name>

The first one sounds more correct to me, as that thing will be called by that name in the current article; however when op reads math texts, the second one seems more common.

Answer 1

In a paper, you qualify any term you invent to be specifically within that paper. If other people adopt your terminology they will refer to your paper.

For example:

[some discussion of the distinctions that lead to a new definition] Herein, we will refer to this property of vector sets as "pseudo-orthogonality".

"Herein" means just in this paper. And then continue your discussion using the term pseudo-orthogonality.

If I need your result, I will cite your paper and its definition of the term in my paper. So I will say

We use the concept of pseudo-orthogonality as defined in [1].

Then my reference is

[1] Carla-Display, "The Clown Murder of Non-Prime Extracts of Large Numbers", Journal of Approximating Numbering Systems, v7.38, 2022, pp 3-11.

Or something like that.

Don't say "will be called", don't say "is called."

Don't raise any expectation your new terminology will be used anywhere else but within your paper.

It is up to other researchers to decide to use your terminology. You should do some due diligence in reading to ensure you are not renaming a known property; thinking you invented it is not enough itself, you want to be sure you did not re-invent it.

It is up to your reviewers to call you out if you have inadvertently done that. And by restricting the use of your definition just to within your own paper, it is still understandable even if you, your peer reviewers and the editor all failed to realize you re-named a known property.

Future lecturers or textbooks will say

What Carla-Display calls "pseudo-orthogonality" was first described in 2021 by Hurling-Cat as "proximate-orthogonality".

Answer 2

Perhaps the second reason is more preferred in textbooks is because it seems more confident in its definition. By using "will be," it's saying what's going to happen (a little more wishy-washy), instead of just doing it.

Answer 3

The tense tells the reader whether you are borrowing a previous concept, or making up a new one.

---

The basics

Borrowing a previous concept

{name} is a concept that is already present in recent literature.

{name} is {description} ({cite the source}).

Making up a new concept

{description} will be referred to as {name} for the remainder of the article.

Note the will be as it is from that point on that this entity is going to be known with such a name.

Note also that use of passive forms tend to be clunky, harder to read and often frowned upon in an academic English setting.

Exceptions

If the new entity is the core of your work, then be clear about it. You could, for instance, open with

We introduce {name-of-entity}, {description}

If you are just packaging a set of definitions to avoid having to repeat it, state it clearly:

Let a {name-of-entity} be {description}