3 ms·
> I would of course explain that the equality sign is not symmetric with respect to such notations; we have 3=A(5) and 4=A(5) but not 3=4, nor can we say that A
by svat 1y ago
> I would of course explain that the equality sign is not symmetric with respect to such notations; we have 3=A(5) and 4=A(5) but not 3=4, nor can we say that A(5)=4. We can, however, say that A(0)=0. As de Bruijn points out in [1, 1.2], mathematicians customarily use the = sign as they use the word “is” in English: Aristotle is a man, but a man isn’t necessarily Aristotle.
— Donald Knuth, Teach Calculus via O Notation (https://shreevatsa.wordpress.com/2014/03/13/big-o-notation-a-couple-of-sources/ https://shreevatsa.wordpress.com/2014/03/13/big-o-notation-a... or http://micromath.wordpress.com/2008/04/14/donald-knuth-calculus-via-o-notation/ http://micromath.wordpress.com/2008/04/14/donald-knuth-calcu...)
- bmacho 1y agoOff: mathematics is kind of moving away from the asymmetric element symbol "∈" to the symmetric type of symbol ":", which, I think is a loss. I'm sad about it. For example with the element symbol you can do let x \in R a real number and you also can do let U \subset R, U \ni 0 a neighborhood around 0 Which you can't do with the type of symbol. I'm probably more picky about the notations following the sound in my head than the rest, but I still think that an asymmetric typeof symbol would be a net win.
- imtringued 1y agoYou must be new to mathematics. There is no standardization. Every paper and book essentially has its own notation system.