My toddler is still learning to speak. We know some numbers now. Today he was counting items on the table, and I quote [with LT->EN translation]:

ZERO
ONE
TWO
THREE

I guess I'm doing something right as a parent. Proud of him and myself .

Why would you do that!? May peace be upon him.

@Lelouch I didn't do anything on purpose. It just happened all naturally. Wasn't even pushing him, he learned and said it all free willingly.

Except now he or she counts wrong

@iiii I wouldn't say he counts wrong as long as he knows it's 4 items even if he starts from 0, the rest is just arbitrary indexation

That's what happens when someone doesn't understand the difference between counting and offsets. But he's still a child.

@matt-jd indexation and counting are different concepts.

@Fast-Nop If you call that "counting" then yes. If you call it "indexing items on the table" - then the kiddo is 100% correct ;)

@iiii 0,1,2,3 and 1,2,3,4 both count 4 items. The only difference is the starting point in the integer space

@matt-jd incorrect. The first one is not 'counting 4 items'. Counting uses cardinal numbers and zero is not cardinal.

@iiii 0 is a cardinal number and happens to be the cardinality of the empty set

@matt-jd With the empty set, there is nothing to count.

@matt-jd I've mixed natural and cardinal numbers. Natural numbers are for counting. Cardinals are for sizes. And natural numbers don't include zero.

@Fast-Nop exactly therefore its cardinality is 0, you can have a look at Wikipedia as well. 0 is among the cardinal numbers.

@matt-jd When there are no items on the table, the toddler won't "count", that's what I meant.

@Fast-Nop that is a good point, I think I will discuss this further with a mathematician friend

Kid doing something cute, not caring about anything... but very likely reacting to positive emotional stimuli from his dad.

I like.

Debating about math and logic.

No like.

Come on, stop being such ... Korinthenkacker.

All that shit shouldn't matter at that age. School comes later, enjoy this time and these precious moments.

Child iterates just fine! 👍😊

@iiii natural numbers sometimes do include zero. Both definitions with and without zero are used.

@electrineer no. Natural numbers do not include zero. N+{0} set is not equal to N. The set is being used, but it's not a set of natural numbers.

@iiii sure, if you want to define it like that.

@electrineer it's not "I want to define like that" it's a mathematical definition of the set of natural numbers 😒

@iiii but it's not the only definition that's in common use. ISO 80000-2 defines it as starting from zero.