Representing Several IF statements inside a FOR loop in Math Notation February 13    1

Representing Several IF statements inside a FOR loop in Math Notation
I wish to correctly represent several IF statements within a for loop in math notation.The FOR loop can be represented as:∀i∈ {0,-,n-1} . (Conditional IF statements) The IF statements apply ...

Some questions regarding open sets and its complement. February 13    1

Let $E^o$ be the set of all interior points of the set $E$.I was able to prove that $E^o$ is always open and $E$ is open iff $E = E^o$.Now I am asked to prove that $(E^o)^c = \overline {E^c}$.Intuitively it is very clear, but I am not sure if my proo

Why is the set of all integers not open February 13    1

A point $p$ is an interior point of a set $E$ if there exists a neighborhood $N_r(p)$ such that $N_r(p)\subseteq E$, and a set is open if all of its points are interior points. Now my question is that since $r\in \mathbb{R^+}$ then why can't we take

Finding the multiplicative inverses of fields February 13

Lets say I have the field $F_{11}$ Why does 2 have the multiplicative inverse 6?In some of the examples I have lets say we are looking $F_5$ why are values up to only 2 considered? So in the example of $F_5$, values $1$, $2$, then $-2$, $-1$ are cons

the set of integers is not open or is open February 13

Baby rudin give the example of the set of all integers being not open if it is a subset of R^2 (I forgot how to code the symbols on this site)If we consider the set of integers in R, is this set also not open? I can find a neighborhood which will con

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