Can M = N+1 if Distance Between Two Vectors = 1

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The discussion centers on the mathematical relationship between vectors in Rn, specifically addressing whether m can equal n+1 under the condition that the distance between any two vectors ui and uj is exactly 1. The example provided involves the vectors (1,0) and (2,0), illustrating that while these vectors maintain a distance of 1, the general case requires further exploration. The conversation suggests that the dimensionality and constraints on vector lengths significantly influence the outcome.

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Is it possible for m = n+1 if there exists u1, ..., um in Rn such that the distance between ui and uj is 1 for any 1 <= i < j <= n?
 
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have a think about the vectors (1,0) & (2,0)

of course things might be different if your vectors ui were of a set length, say 1
 

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