Zero is Old New(s)

I’m reading “Zero: the biography of a dangerous idea” by C Seife.

It starts off telling us about the properties of 0. And thus how weird it is.

But, it never tells us why such mathematical properties are such.

For example: Why does 0 x 4 = 0 ?

A quick search on the web got me:

I’m sure there are other answers, but I feel that this one gives us a very usual one.

Perhaps you math people can give us a better answer. I think that guys answer is plain incorrect; I absolutely can visualize zero times: it is what is still there. .

In my example: 0 x 4 should equal 4 Becuase I have multiplied 4 by nothing, by an absence, a blank spot, a place holder.

If I do nothing to something I do not end up with nothing. On the contrary: I still have what was there.

Just the same: if a have zero times something, I have not done anything with it or to it. Zero of something is something, if anything, it is zero. Which is still some thing.

It is zero. In reality, though. If there is a can of peanuts, and I attempt to multiply it Zero times, I have the can of peanuts.

It seems math as based in a particular fantasy that defies reality, rather, it makes us believe that reality is not what we see it as.

Similarly, if I divide a number by zero: I should get the number itself.

A pie divided by zero should equal the whole pie, not an irrational or infinite pie that can’t be eaten, Enjoyed or digested.

Any thoughts ?