Everybody experienced writing irrational numbers using decimal notation in school, so those definitely count.
I've seen them expressed as letters or formule
You've proved my point. It's either π or 3.14. Except that the latter is a rational number :)
Weird, I just assumed that was normal in most education systems. I don't know how you'd get a sense of the rough scale of various common irrationals, without having some idea what they look like when represented in decimal notation. Such representations are normal starting not later than when we start seriously working with circles, in US school, and never really stop coming after that. Estimation exercises lean heavily on having some idea of the decimal representation.
> You've proved my point. It's either π or 3.14. Except that the latter is a rational number :)
Never claimed π is 3.14, so no, I didn't at all prove your point. I wrote that it's very well known that it starts that way. When a normal person says "decimal number" they mean to include π, because any usefully-precise decimal representation of it's going to involve a decimal point. At least in the US, they saw it represented "3.14..." or "3.1459..." or whatever, many, many times in school. It's obviously, to a non-mathematician, a "decimal number". They mean "the real numbers" (or, perhaps, depending on context, exclusively the parts of the reals that aren't whole integers), except that name is harder to remember than the incorrect (but more common and intuitive) "decimal numbers".
For me a "decimal number" is a number represented in base 10. Which is why I was asking. I even googled and there is no real definition.
I'm currently reading one. Looking good so far. I'll let you know after I finish.
To be pedantic, we experienced writing approximations of these numbers in decimal arithmetic.
“Decimal numbers” is not a term routinely used in mathematical circles, 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, quite reasonably, interpret “the Decimal numbers” to mean all numbers that can actually be expressed with decimal notation, in which case you are talking about (a subset of) the rationals.
It is extremely important, when discussion different sets, to be clear about the difference between these two.
if not then they are equal, if yes then there are more decimal numbers between 0 and 1 than integers.