Ouch. Worst I have done is break three pieces of glassware in a chemistry lab.
I do not mind applied. "we do not have to worry about this solution as it has no physical meaning, so we can let the mathematicians ponder over it."
But I hate oscillopscopes and electric stuff. When I chose my labs, I do my best in avoiding both.
The one thing I like about pure math is the lack of numbers
And wow so many strange objects, stuff without a zero element, those have got to do some weird things.
And all is well. I know enough people taking math as I study physics. One of them is always doing her maths assignments in our lectures.
Thanks for clarifying that. Not sure about the pass rate here but I have a feeling that they scale many people up. I heard the story of an exchange student taking 4 maths subjects. They spent their time here not enjoying kangaroos and koalas but doing maths assignment after maths assignment.
then you will often seen identities in the relevant axioms, but for the Set of Natural Numbers (Often a funny N with two lines) identities aren't needed. Like in most sets.
Some mathematicians include 0 in the Naturals for a sense of completion. Often a * is put in front of sets to mean the set without the zero element. Q* is the rationals without 0. Z* is the integers without 0.
Whenever you group together numbers, you don't need identities because there are no axioms requiring there to be identities. Sets don't need additive identities since they are just a big bag of things.
When you have a system such as a Vector Space, Metric Space, Normed Space, Ring or Group, where there are things happening to your elements,
Super scary as in the average mid semester exam mark for a course called analysis 1 was in the 30-40% range...
I sort of miss being able to prove things as I switched to applied.
Hmm question is 0 an element of the natural numbers? Do they need an additive identity?