Understanding 0

I am (obviously) not a math person but still have been trying to understand how 0 works such as x*0=0. This does not seem to me to be logical. 0 is not a number rather it represents the absence of any value - it is nothing. In physics when something is acted upon by nothing then nothing changes but in math when x is acted upon by nothing (x*0) then x disappears (x*0=0)? How does x become nothing when nothing has acted on it? By logic x+0=x, x/0=x, x*0=x and 0/0=0.

 

It's not "acted upon", it means the value zero times, which is why the answer is always 0.
2 x 2 means 2 twice (4), 2 x 1 means 2 once (2),and 2 x 0 means 2 0 times, which is 0.

Does that make more sense?

 

Zero is a digit and thus it is a number. A number without value but nonetheless a number. Your thread demands a deeper understanding of mathematics that I cannot help you with.

You said:

By logic x+0=x, x/0=x, x*0=x and 0/0=0.

x + 0 = x...correct.

x/0 is undefined not x. We cannot divide by 0.

x • 0 = 0. Zero times anything is nothing.

0/0 is not 0. It is called an indeterminate form.

Search online for a history of zero and real numbers.

 

"0" is defined as the "additive identity". That is, x+ 0= x for any number x.
We also have the "distributive law" for arithmetic: a(b+ c)= ab+ ac for any numbers, a, b, and c.

In particular a(b+ 0)= ab+ a0. But since b+ 0= b, a(b+ 0)= ab so ab= ab+ a0. Subtracting ab from both sides 0= a0.

 

Original question dated 3/21/18.

 

And in all that time hadn't got a decent answer!