T488 tweak

Author: prabau

theorems/T000488.md

@@ -11,4 +11,5 @@ refs:
     name: Every sequence has a monotone subsequence
 ---
 
-Every sequence in a totally ordered set has a monotone subsequence (see for example {{mathse:1706258}}). The space being {P19} implies that this subsequence has an accumulation point $x$.  And because the subsequence is monotone, it converges to $x$ because every order-convex neighborhood of $x$ contains eventually the subsequence as it contains infinitely many terms of it.
+Every sequence in a totally ordered set has a monotone subsequence (see for example {{mathse:1706258}}). The space being {P19} implies that this subsequence has an accumulation point $x$.
+And because the subsequence is monotone, it converges to $x$ because every order-convex neighborhood of $x$ contains a tail of the subsequence as it contains infinitely many terms of it.