The correct mathematical term is “real number”.

Yes, but you'll see "decimal" more in the wild, and that's what people mean by it. "You write it with a decimal point", and they do usually mean to include the irrationals. So, yes, real numbers, but the reasoning behind their usage is "you write it with a decimal point". I'd bet more people understand "decimal number" used in that sense, than understand "real number".

i've never seen an irrational number written in digits in my whole life. Have you?????

I've seen them expressed as letters or formule

Never. Never in school? It's totally normal in the US, it's the reason as many people know that π starts "3.14" as do.

Yes never, not in school, not in analysis, and certainly not in numerical analysis.

You've proved my point. It's either π or 3.14. Except that the latter is a rational number :)

> Yes never, not in school, not in analysis, and certainly not in numerical analysis.

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".

Can you write here an irrational number, not in the form of a letter or a formula?

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.

3.14...

Isn't that equal to 157/50?

> i've never seen an irrational number written in digits in my whole life. Have you?????

I'm currently reading one. Looking good so far. I'll let you know after I finish.

> Everybody experienced writing irrational numbers using decimal notation in school,

To be pedantic, we experienced writing approximations of these numbers in decimal arithmetic.

It’s not just pedantic! It completely changes the answer to the question.

Do you actually think I meant otherwise? Like, actually? Do you think anyone on HN was confused about it? Did you really think that?

Yes, I thought you meant otherwise. Yes, I was confused about it. Yes, I really thought that. Truly.

You truly thought I didn't realize that "3.14" is an abbreviated representation of π, or that I somehow missed years and years of using the "repeating" sign above various decimal representations, or all those "..."s, such that it was plausible I meant the obviously-wrong thing rather than the correct thing? This stuff is hammered in in US K-12 school.

You really are being mean about someone trying to help you. Not sure why.

“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.

Nobody ever finished writing an irrational number in school.

sqrt(2)

… Using decimal notation.

Goodness this is like talking to GPT at times.