You really are being mean about someone trying to help you. Not sure why.
“Decimal numbers” is not a term routinely used by mathematicians (quite distinct from primary and secondary teachers of arithmetic who are, unfortunately, rarely mathematicians), precisely because of the confusion you, perhaps unwittingly, elicited. If you mean by this phrase all infinite series with a decimal approximation, then you’re talking about the reals. Some people thought you meant this!
Other people, also quite reasonably, interpret “the Decimal numbers” to mean all numbers that can actually be expressed with (finite) decimal notation, in which case you are talking about (a subset of) the rationals.
It is extremely important, when discussing different sets, to be clear about the difference between these two.
“Decimal numbers” is not a term routinely used by mathematicians (quite distinct from primary and secondary teachers of arithmetic who are, unfortunately, rarely mathematicians), precisely because of the confusion you, perhaps unwittingly, elicited. If you mean by this phrase all infinite series with a decimal approximation, then you’re talking about the reals. Some people thought you meant this!
Other people, also quite reasonably, interpret “the Decimal numbers” to mean all numbers that can actually be expressed with (finite) decimal notation, in which case you are talking about (a subset of) the rationals.
It is extremely important, when discussing different sets, to be clear about the difference between these two.