# B What is math without 0 like?

1. Nov 18, 2015

### Alanay

It's something I've been thinking about recently, would math be simpler or way more complicated without 0?

1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21...

I've been trying to do some simple equations without 0, and with small numbers the results are usually the same. But would getting rid of 0 solve any problems, for example dividing 0 by 0. I'm not sure how much this has been thought about before and if there has been any reasoning why this would be a terrible idea so I'd like your guy's opinions on the matter.

2. Nov 18, 2015

### Staff: Mentor

3. Nov 18, 2015

### Staff: Mentor

"People first could handle their crop through counting and adding. But as soon as they started borrowing crop, they had to turn to negative numbers to get theirs accounts balanced. Necessary for it was by the way the discovery of zero, which wasn't easy at the times. Why should one count nothing? It took a while."

Eliminating the 0 is nothing else than counting. It has nothing to do with calculation, computing or any modern science any more.
You could ask as well how it would be if we only can count to 5 since we have just 5 fingers. But even the Neanderthals could count further ...

4. Nov 18, 2015

### micromass

OK, but this is actually irrelevant. You can have 0 as a placeholder and still not accept the existence of 0 by itself. In fact, that is what most ancient civilizations actually did.

5. Nov 18, 2015

### rootone

(Although I expect some of the soldiers who didn't get paid after losing a battle were well able to grasp the concept)

6. Nov 19, 2015

### Svein

There are at least answers to this:

7. Nov 19, 2015

### micromass

8. Nov 19, 2015

### pwsnafu

We don't know of any Roman numeral for zero before 725 (which is first use of N for zero we know of). We do know that the word nulla was used for the concept.

9. Nov 19, 2015

### 256bits

You had as many apples as you had before you went apple picking. Why go through all the trouble of recording no change?

10. Nov 19, 2015

### PeroK

You'd lose associativity:

$(2 + 1) - 1 = 3 - 1 = 2$
but
$2 + (1 - 1)$ would de undefined.

We already have to take care that a denominator is not 0, and this would extend to everything. If you have $x-y$ anywhere, you'd have to exclude the case $x = y$.

$cos(\pi/2)$ would be undefined. But, then $tan(\pi/2)$ is not defined and we manage that.

Losing the concept of zeroes of a function would be a major loss, I would say.

I'd prefer to exclude a number like 673, since that doesn't turn up very often. Missing out 673 would be much easier to deal with.

11. Nov 19, 2015

### FactChecker

If I had $5 and owed someone$5, what would my net worth be? How can simple calculations be done without 0? In abstract algebra, the simplest thing above a "set" is the "group". A group requires an "identity" element, which, when added to another number, causes no change. That is 0. Without that it is not possible to do even the simplest math.

12. Nov 19, 2015

### Alanay

You could use a placeholder or simply not write anything at all. You can do even the simplest of math without 0.

13. Nov 19, 2015

### PeroK

You can do a lot of maths without 673. Even more than you can do without 0.

14. Nov 19, 2015

### Svein

Then how would you detect the difference between "haven't written anything" and zero?

15. Nov 19, 2015

### Alanay

Okay, sure but that wasn't the topic. Although now I'm curious why 673 is so useless. Does it just not appear much in any equations?

16. Nov 19, 2015

### PeroK

Have you ever used the number 673?

17. Nov 19, 2015

### Alanay

You could do something like

net worth:

I know using a placeholder would be better, but wouldn't having no 0 in equations save much room on the whiteboard. We can still define variables with a placeholder or just the word nothing/empty or something more technical if you prefer.

18. Nov 19, 2015

### Alanay

Good point.

19. Nov 19, 2015

### Svein

Yes, of course, we mathematicians are a lazy lot. It is much easier to write "0" than "nothing".

20. Nov 19, 2015

### Alanay

I understand. I'm not talking about when defining the value of something with 0. I'm talking about larger numbers and simply not showing anything if it has no value. We could even just use 0 as a placeholder but get rid of 10s, 20s etc.

21. Nov 19, 2015

### PeroK

Here's a thing. You'd have to change all the computers and all the computer systems to stop them using 0. You can't have computers doing things like:

$5 + 0 + 1 + 6 = 12$

If people aren't allowed to use 0. If a computer can add four numbers together, one of which is "0", then why can't I?

You'd have to forbid 0 being entered in a numeric field, as it isn't a number. It would be just as meaningless as entering "a" in a numeric field.

22. Nov 19, 2015

### Alanay

Because it's almost redundant, what's the point of adding a value of nothing.

23. Nov 19, 2015

### Staff: Mentor

+++ Breaking News +++ Sieve of Eratosthenes actually a sieve +++

24. Nov 19, 2015

### Svein

But if you have an expression like 5+p+1+6=12 and you want the value for p that satisfies the equation, what would you do? The obvious result is p=0, but if we are not allowed 0, you would either write p= or "p is nothing"...

25. Nov 19, 2015

### PeroK

Because it's there! That might be the sales from your four salesmen. The second salesman didn't sell anything, so you enter 0. If you can't enter 0, then the program can't simply add the four numbers together.

You really, really don't like 0 do you?

Also, if the figures were profit and loss and they were:

$+3 - 5 + 2 + 7$

Then the program would blow up $+3 - 5 + 2 = -2 + 2 =$ error; invalid arithmetic operation

You simply can't add those four numbers if 0 is not a valid number.