The mysteries of the zero divides

Below I will present the "evidence" how zero multiplied by infinity equals 13 and zero divided by zero equals 7. We shall start with a simple question, which most people without thinking use to answer very quickly on.

1) What is one divided by zero (1/0) equal to? If you put this question to the common people (at least in Sweden), the answer uses to be either 1 or 0. As both answers are wrong, let's do an investigation. We set up a division 1/x and thereafter we make x to shrink from 1 to 0 by letting it takes the values 1, 0.1, 0.01, 0.001, and so on and see what happens. The dear reader my check him or herself using a calculator. Thus:

1/1 = 1
1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000

We use to say that the quote increases beyond all limits when x approach zero. Or, (more in exactly expressed)

1/0 = inf (I have no sign for "infinity", so I use "inf" instead).

2) Now if the quote 1/0 = inf, then the quote between any other number (with one exception, I will mention that further down) than 1, for example 13, and zero will equal infinity. Let's do a similar arrangement as above. Thus:

13/1 = 13
13/0.1 = 130
13/0.01 = 1300
13/0.001 = 13000

…and in other words

13/0 = inf

3) Now, look at a normal division, for example 12/4 = 3. If we multiply both side with 4 we obtain

12/4    =    3
4*12/4 = 4*3
12     =    4*3 (having made an abbreviation on the left side).

If we do the same with 13/0 = inf we obtain

13/0    =    inf
0*13/0 = 0*inf
13     =    0*inf

Thus we have showed "how zero multiplied by infinity equals 13"!

Now there is only one crucial thing with the above evidence.

IT IS ABSOLUTELY FORBIDDEN TO PERFORM A ZERO DIVIDE

That's because 0*inf can equals everything. This product is undefined. In other words, when the emptiness and the infinity come into touch with each other, everything can happen.

However it is allowed to say that 1/x tends to infinity when x tends to zero. Further more that 1/x tends to minus infinity when x tends to zero from the minus side (-1, -0,1, -0,01,
-0,001 etc). However standing exact on the zero you can't say if the infinity is positive or negative! Or maybe it will be that infinity has transcended the positive and negative categories!

The special case 0/0
This division must not equal infinity. It can equal everything. In other words, it's as undefined as 0*inf. It can for example equal 7. Evidence:

0/0 = 7
0*0/0 = 0*7
0 = 0*7 (after abbreviation with 0 on the left side).

In other worlds, we can say that the nothingness in the numerator in some way is 7 times bigger than the nothingness in the denominator!

Take care, and don't get lost in the big universe between nothingness and infinity And I am NOT a mathematician