Is it correct to say that $0$ is not $100$% of $0$?

Question

$n = 100$% of n

if $n=0$ then $0 = 100$% of $0$, but

$0 = 1$% of $0$, $0 = 2$% of $0, 0 = 3$% of $0$, etc

Is it correct to say that $0$ is not $100$% of $0$?

Answer 1

There is a subtlety here not captured in the other answers. If we say that $a$ as a percentage of $b$ is $$\frac ab \times 100\%$$ then $0$ as a percentage of $0$ becomes $$\frac 00 \times 100\%$$Now $\frac 00$ is undefined, and in general we cannot divide by zero, so the percentage is strictly undefined. The subtlety is the division by zero which is concealed by the language about percentages.

The language about percentages is, to be sure, often used less formally than the defined operations of arithmetic. The extent to which this matters therefore depends on the formality of the context.

Answer 2

I think if you go this way, you may say : $0$ is not only $100\%$ of $0$.

Answer 3

By your reasoning, $4$ is not $1+3$ because $4$ is already $2+2$. Nope. $4$ is both $1+3$ and $2+2$, and of course many other things like $8 \div 2$.

Answer 4

Every percent of $0$ is $0$. So, no, it is not correct to say that. $0$ is $100\%$ of $0$.