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An important facet to mathematics in general, that most are unaware of before studying it, is that the majority of proofs, especially those done in bachelor uni
by blattimwind 9y ago
An important facet to mathematics in general, that most are unaware of before studying it, is that the majority of proofs, especially those done in bachelor university courses, are purely notation. Other problems often become trivial to solve by using a different notation (e.g. polar form vs. points on the complex plane) as well.
- isolli 9y agoWhat do you mean by that?
- Silhouette 9y agoAn important facet to mathematics in general ... is that the majority of proofs ... are purely notation. To the extent that this is true, how much do you think that is due to the notation itself, and how much is due to someone identifying the essential underlying concepts and then making those the basis for a good notation?
- yomritoyj 9y agoCould you please elaborate. Just to take two elementary examples: the intermediate value theorem and the theorem that any two bases of a finite-dimensional vector space have the same number of vectors. I would have thought that both require mathematical ideas and not just notation.
- gpawl 9y agoI think what you mean is that most proofs follow easily once proper definitions are chosen. Notation is a visualization of definitions.