Now zero is an extremely useful number. OK, it is useful but it is not really a number. It is just a place marker to say nothing is there. It really helps when writing numbers, just like the comma. Take the numbers 1,124 and 1,024 for example. When you say them aloud, you say ‘One thousand, one hundred and twenty four’ and ‘One thousand and twenty four’. Saying ‘Zero hundred’ would not add any information to 1,024. Zero is just a place marker to tell you that there are not any hundred units in the number 1024. There is 1 x thousand unit, 2 x ten units and 4 x 1 units. So let us be honest, zero is not really a number. The primary function of numbers is to count and you cannot count zero of anything because there is nothing to count. As for dividing by zero, see where that gets you.
Scientists tend to use BCE (Before Common Era) and CE (Common Era) instead of BC (Before Christ) and AD (Anno Domino). So we know when the years 1 BCE and 1 CE happened but what happened to the year 0? We know where 0 is on the number line but when was the year 0? It is not on the Roman calendar. Maybe this is why a person’s age was calculated in Korean as starting as 1 when she was born.3
So adding zero to a number leaves it the same. This sounds sensible. Multiplying a number by zero leaves us with zero. Supposing you have 2 apples and you add 2 more and then add 2 more, you will end up with 6 apples. This is the same as multiplying 2 apples by 3. This makes sense. However if you have 4 apples and you add 4 apples zero times, you still end up with 4 apples. So zero is a bit awkward with multiplication. Of course, multiplying 4 by 0 is interpreted as adding 4 to 0, 0 times giving 0. It seems more a convenience that multiplying by zero results in zero. Being able to multiply by 0 helps find many solutions to mathematical problems but it seems to lack the purity of most mathematical concepts. As mathematics is a system, the operation of multiplication by 0 can be defined as required by the system designers. You can multiply by 0 but you definitely cannot divide by zero.
I have been suspicious of the way zero facilitates proofs. The proof that the product of two negative real numbers is a positive real numbers uses zero as follows:
Given two positive real numbers a, b:
Showing that the product of two negative real numbers is a positive real number as the product of two positive real numbers is a positive real number. It uses a clever mechanism with zero to introduce the term –b on th
