existence of moments question
I was ready the book "Introduction to probability theory" by James R. McCord, III [and] Richard M. Moroney, Jr and it gave this thereom about the existence of moments: if the mth raw moment of a random variable X exists, then the Xth and all preceding moments of X about any finite point all exist.
It then said that this follows from simple computations and the relation:
E(|X|^(m-1))≤|X|^(m + 1)
Which is true because: |x|^(m-1)≤|x|^(m+1).
For all real x and all m≥1.
I am not understanding any of this at all!!! Can someone help explain to me what is going on?