Things that puzzle me: 2 different signs

When I was a first-year student I had a very nice friend who had been to a very good school.We used to study together and at the end of the year, just before the exams she asked me a question.
It involved the Greek letter alpha  and the sign for infinity which looks like the number 8 lying on its side,
Alpha is open at one side, the sign for infinity is not.
I realised that all through the year she had thought they were the same.Much of what we did used these signs.So how had she  sat through lectures and seminars without understanding,
I feel a lot of children at school must be in a similar situation.It must be hard for them