At a glance, deciding whether 13.8 or 13.11 is larger should not be especially difficult. When people get it wrong, it usually is not because the problem is deep; it is because they do not stop to think. They hesitate for a moment, get confused by the notation, and then confidently jump to a conclusion.
This kind of argument appears online all the time. Every so often, people end up fighting over some basic numerical or mathematical question. A few years ago, one of the most common examples was whether repeating 0.9 is equal to 1. Another example was a post meant to test people’s grasp of elementary inequalities:
1.假设：a＞b，则a≥b必然成立。2.假设：a≥b，则a＞b必然成立。
Some insist that repeating 0.9 must be less than 1. If they have never learned the idea of limits, their intuition tells them that no matter how close a number gets to 1, it is still smaller than 1. At that point, bringing out a university math textbook will not persuade them. Even if some long-dead mathematician rose from the grave to explain it, they still would not accept it.
The same thing happens with statements like a≥b. Some people never properly learned the concept in school; others learned it once and forgot it as soon as they put their textbooks away. So it is not surprising that they mix up the relationship between “greater than” and “greater than or equal to.”
Really, this is true of many things, not just math. Either you know something or you do not, and for most people that gap in knowledge does not prevent daily life from going on. Everyone is ignorant in the face of the vastness and complexity of human knowledge. If someone wants to fill in a blind spot, that is worthwhile. If not, that is their choice.
But when you are standing in front of your own weak spot—or in front of people who actually know the subject—a little caution and humility never hurt anyone. What does make a person look ridiculous is charging ahead with the fearless bravado of ignorance and trying to argue by force where understanding is missing.