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Results tagged with definitions
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user 29316
24
votes
Nonequivalent definitions in Mathematics
$(a,b)$
Is that a coordinate pair representing a point in the plane? or,
The open interval from $a$ to $b$? or
The greatest (highest) common factor (divisor) of $a$ and $b$? or
The ideal genera …
11
votes
4
answers
2k
views
Why do mathematicians prefer one definition over the other when they both define the same co...
Here is a basic, though very important, example:
Hilbert takes as primary the notion of “congruence” (or “equal”) between segments. His first axiom of congruence “requires the possibility of construct …
- 2,437