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Comment by pmontra | Hacker News Reader

The gist of it seems to be: intuitively zero is nothing and not a number but eventually you discover that it's useful to think about it and use it as a number so you change your mind, maybe without even noticing.

By the way, some kids misunderstood the digit zero for the number zero.

> “Yes, you already asked me! It’s a number for nothing. You can use it to make 100.”

> “Yes, you already asked this! It’s in the number 10, so it must be a number. We don’t mix shapes like this.”

Imagine the surprise if told that A, B, C etc are also numbers :-)

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> By the way, some kids misunderstood the digit zero for the number zero.

That's not a misunderstanding. Place-value notation requires that digits are numbers. The fact that 10 is a number doesn't mean that the 0 within the 10 is not also a number; the kindergartener is correct in saying that that location means the 0 is a number.

They’re also correct in saying it represents pure, unadulterated nothingness though. The teacher is confusing number theory with reality by limiting them in the way she does.

> They’re also correct in saying it represents pure, unadulterated nothingness though.

This makes me hesitate. For example, if I ask you how many quiches there currently are in your refrigerator, it does not follow that nothing is currently in your refrigerator. The zero is bound to the unit it measures.

Not in an empty universe.

I agree, I thought a lot of the "before" answers were excellent and insightful. The teacher did these children no favors by foisting such a meaninglessly pedantic distinction on them at this young age.

> “When we ask ‘how many,’ the answer is a number.

How about a few is a few a number?

Fun way to look at it. In Common Lisp, NULL is not a number. But in Assembly language, it absolutely is.

Is "no" a number? As in "I have no apples." It is strange that we can't say "I have yes apples" otherwise.

> It is strange that we can't say "I have yes apples" otherwise.

You do see ungrammatical "yes" applied sometimes when people are stumped as to how to indicate the opposite of a negative sentence.

It is not strange in general that certain things are, for no apparent reason, impossible to say. That occurs in every language. English modal auxiliaries, for example, do not have non-finite forms, so in many sentences it is mandatory to replace modal can with lexical to be able [to...]

I concede that my opinion is worth very little to nothing and I didn't even check what's the mathematical consensus on this matter, but when one sees that 1100, 110, 30, 22, 20, 15, 14, 13, 12, 11, 10, A are all the same number one starts thinking about the difference between symbols as numbers and symbols as digit.

I hopefully didn't make mistakes in the several representations of twelve.

> I hopefully didn't make mistakes in the several representations of twelve.

That depends! What is the numeric value of A?

And then: how can you answer that question without admitting that A is a number?

You probably meant "C" as the final one, instead of "A": https://www.wolframalpha.com/input?i=12+in+base+13

Yeah, a made a mistake on the easiest base

That's the argument in a nutshell. Is 10 a single number, or two numbers? In context, it is one number. But I digress because typing it out suggests it is two.

Would you rather have $100.00 or $0100?

Digit is a symbol, number is a concept. It’s a map-territory distinction. While a single digit can be used to represent a numerical value, it isn’t a number per se.

You can’t really use the number 0 to make 100.

Imagine the surprise learning that anything other than combinations of 0's and 1's are not numbers. For the same reason, but more extreme and in the other direction.

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