Both ways are just notation. There’s nothing more real about 3/10 compared to 0.3.
Telling you otherwise might have worked as a educational “shorthand”, but there are no mathematical difficulties as long as you use good definitions of what you mean when you write them down.
The issues people have with 0.333… and 0.999… is due to two things: not understanding what the notation means and not understanding sequences and limits.
Telling you otherwise might have worked as a educational “shorthand”, but there are no mathematical difficulties as long as you use good definitions of what you mean when you write them down.
The issues people have with 0.333… and 0.999… is due to two things: not understanding what the notation means and not understanding sequences and limits.