How would i visualize the set to be able to understand and answer this question

Question

Let $A$ be the set of all people who have ever lived. For $x, y \in A$, $xRy$ if and only if $x$ and $y$ were born less than one week apart. Determine:

(i) Whether or not the relation $R$ is reflexive;

I understand that $x$ is in relation to $y$ if $x$ and $y$ were born less than one week apart, but how would you mentally visualize this relation to be able to answer the following question, and when answering the question do I answer for when $x$ is in relation to $y$ and when they aren't in relation or just assume that they will always be in relation?

Answer 1

If $xRy$ iff $x$ and $y$ were born less than one week apart, we have that $xRx$, for all $x$, because $x$ is born exactly the same day of $x$.

See Reflexive relation :

In mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself. In other words, a relation $R$ on a set $A$ is reflexive when $xRx$ holds true for every $x \in A$. Formally, when :

$∀x \in A, xRx$ holds.

Answer 2

When answering the question, you only care about $x,y$ such that $x=y$. Has anybody ever been born more at least a week before or after the day on which s/he was actually born? It's ridiculous, right?

You can visualize this as a calendar, starting about 100,000 years ago and stretching, oh, let's hope far into the future. Each day of the calendar is filled with the name (/rank/serial-#/DNA-encoding/...) of every person ever born. The cells, and thus the calendar, can be pretty big. Let's say it's a daily calendar, and it's one continuous scroll, no separate pages. Then $x,y$ are born on the same day iff they appear in the same cell; they're born a day apart if they appear in adjacent cells; they're born at most two days apart if they appear in the same cell, adjacent cells, or in cells that are two apart; they're born at most three days apart if the distance between the cells they appear in is at most $3$; ... .