So, I think the author meant that a real number is actually a sequence of approximations towards an ideal. So, 0.5 has infinite sequences like 5, 3, 2, 1, 3/4,

So, I think the author meant that a real number is actually a sequence of approximations towards an ideal. So, 0.5 has infinite sequences like 5, 3, 2, 1, 3/4, 1/4, 3/5, 2/5, 1/2