In Reply to: decimal system handout posted by Alex on January 20, 2003 at 12:00:56:
>the decimal system handout: second definition on page2,
>"Let 0_1,..., x_n" instead it should be "Let x_0,..., x_1" if i >understood the definition correctly.
Thanks!
>the end of the first example on page 30 of week 2's notes, is
> missing a closing parenthese, which it should read (Merely...
> to have an upper bound.)
Thanks!
> and that on top of page 35 "...infimum of E and is denoted inf E" ?> should there also be () around the E in consistent to the notation
>sup(E).
OK, I should made clearer that the parentheses are optional for inf
and sup. It's like sin, log, etc: both sin(x) and sin x are
valid mathematical expressions, and the same is true for sup and inf.
Thanks though.
>also, the first sentence on page 32 from week 2's notes: it Well, I will make the change, however it is standard mathematical "There exists an element x in the set S" may be abbreviated as "There exists x (- S" (where (- is supposed to represent the "element of" symbol), while "There exists an element x such that 2 < x < 4" can be abbreviated "There exists 2 < x < 4" and should be read "there exists an x between 2 and 4". I agree "There exists x < y" may either mean "there exists an x less than y" or Terry
>reads "some natural number 0
practice to combine the introduction of a variable with the
domain of that variable, for instance
that sometimes this may be a little confusing, since a statement
such as
"there exists a y greater than x". However, which one of the two
is meant is usually clear from context because one of the
variables x,y should already be defined, while the other one is not.