Questions tagged [definition]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
0 answers

What does P. G. Tait mean by "double points"?

I am reading the following short paper: P. G. Tait. Some elementary properties of closed plane curves. Messenger (2) 6 (1877), 132–133. JFM 09.0393.01 Here, Tait writes The closed curves ...
user avatar
4 votes
0 answers

Why did the mathematical community settle on these properties to define a topology?

The following post is long, but I decided to write more rather than less in case it's helpful. I tried to make it clear, quick, and easy to skip to the short version of my question, so the reader can ...
user avatar
  • 471
0 votes
1 answer

Motivation behind original definition of metre? [duplicate]

The first original definition of the metre, presented by the French Academy of Sciences in 1795 is: The length of the metre is one ten-millionth of the Earth quadrant, the distance from the North ...
user avatar
  • 141
2 votes
1 answer

History of the definition of complex derivative

Almost all of modern complex analysis (Cauchy residue theorem, analytic continuation, etc) depend on the definition of a complex derivative. That definition requires the derivative at a point $z_0$ is ...
user avatar
  • 355
3 votes
1 answer

When were equivalence classes formalized?

Neither wikipedia or the first few pages of Google are showing me much about the history of the development of equivalence classes. When was this notion first formalized? Footnote: I originally asked ...
user avatar
  • 299
1 vote
2 answers

What did Euclid mean by a straight line in his time?

The third and fourth definitions in Euclid's Elements say: The ends of a line are points. A straight line is a line which lies evenly with the points on itself. The fourth definition is usually ...
user avatar
5 votes
1 answer

Definition of ordinal multiplication

The ordinal multiplication $\cdot$ can be defined recursively via ordinal addition $+$ for any ordinal $\alpha$ as follows: $\alpha\cdot 0=0$. $\alpha\cdot (\beta+1)=\alpha\cdot \beta+\alpha$ for any ...
user avatar
  • 545