# has/lies at a minimum distance from

#### li_mo

##### Senior Member
I have a doubt about the correctness of the following sentences. Would the following ones be correct (and make sense)?
1. We refer to the math object A that has the minimum Euclidean distance from the math object B.
2. We refer to the math object A that lies at the minimum Euclidean distance from the math object B.
For some reason, I would like to avoid something like "We refer to the math object A that is the closest to the math object B". I would like to keep the "minimum Euclidean distance from" part, if possible.

Note: about the context, both "math object A" and "math object B", are just sets of ordered data, like math sequences.

• Note: about the context, both "math object A" and "math object B", are just sets of ordered data, like math sequences.
Your note suggests that your statements refer to a math problem that is not of a geometric nature but more of a mathematical nature where you transform those sequences into a virtual Euclidian space, i.e. into an orthogonal and linear plane (or into one-dimensional, flat, linear space.)

If so I prefer:
We refer to the math object A that has the minimum distance from math object B (among all sequence-pairs within the set).

When you say "lies at the minimum distance", I'm automatically imagining a physical flat plane, which automatically gives the statement a more geometrical nature and feel.

PS: I'm not an active mathematician. I just vaguely remember some things from university and hear (casual) math terminology from other engineers and programmers quite often.

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I have a doubt about the correctness of the following sentences. Would the following ones be correct (and make sense)?
1. We refer to the math object A that has the minimum Euclidean distance from the math object B.
2. We refer to the math object A that lies at the minimum Euclidean distance from the math object B.
For some reason, I would like to avoid something like "We refer to the math object A that is the closest to the math object B". I would like to keep the "minimum Euclidean distance from" part, if possible.

Note: about the context, both "math object A" and "math object B", are just sets of ordered data, like math sequences.
I think both are okay, but agree with manfy.

Maybe: We refer to the math object A which is at the ...

???

Thanks both for your nice replies and comments! Yes, both "has" and "which is" are fine with me... Many thanks!!