2010年10月25日 · Based on logic, an axiom or postulate is a statement that is considered to be self-evident. Both axioms and postulates are assumed to be true without any proof or …

Terence Tao (Analysis I, p. 25, n. 4):From a logical point of view, there is no difference between a lemma, proposition, theorem, or corollary - they are all claims waiting to be proved.

Now, if you look at this proof you notice that I have used many other theorems to prove this. Thus we call this specific result a corollary. However, I'm sure I don't have to say this, but just in …

2018年5月5日 · Per your second question, virtually every book on introductory functional analysis would contain the corollaries you're after. To name a few that I like, Rudin's book Functional …

2016年1月13日 · The two corollaries of Stoke's theorem is as follows: 1) $\int \left ( \vec{\nabla}\times \vec{v} \right ).d\vec{a}$ depends only on the boundary line, not on the …

2022年4月19日 · How can I prove the following 3 claims? Or, if possible, could you provide suggestions for how I could prove them?

2019年9月27日 · One of the first corollaries of Lagrange is that every group of prime order is cyclic. This is not equivalent to Lagrange. Lagrange's theorem can also be used to show that …

2023年11月1日 · Quite often there are alternative places to start which turn out to be equivalent once they are understood. It is more important to understand how the corollaries are derived …

I am learning functional analysis and the Hahn-Banach theorem right now, but cannot wrap my head around the idea of norms of bounded linear functionals and dual spaces for some …

I'm having difficulty understanding the relationship between two corollaries in Lang's Algebraic Number Theory, on page 16 for those with the book. They can also be found in his Algebra. …