An example of simultaneous equations.

In an atom, there is proton and a neutron.

In protons and neutrons, there are quarks. There are different kinds of quarks, one up and one down. These carry the electrical charge.

A proton has a charge of +1.
A neutron has a charge of 0.

In a proton there are two up quarks, and one down quark.
In a neutron there are two down quarks, and one up quark.

By using simultaneous equations, one can find the charge of each quark.

2u + d = 1 (proton)
u + 2d = 0 (neutron)

double the neutron equation, to get

2u + 4d = 0
take the other equation...

2u + 4d = 0
-2u + d = 1

3d = -1
d = -1/3

so a down quark has a negative 1/3 charge.

Take this value and put it in an equation...

2u + d = 1
2u + - 1/3 = 1
2u = 1 and 1/3 = 4/3
u = 4/3 divided by 2.
u = 2/3

So an up quark has a positive 2/3 charge.

up = 2/3
down = -1/3

You can substitute these values to test the validity.

Why does 1/0 make infinity?

If 1 divided by 0 makes infinity, it means infinity times 0 is one. But zero doesn't add up to anything. Or does it?

Divide 1 by 3, using long multiplication. It will come to 1/3, or 0.333333333333333.....
note that the line of threes is infinite.

Now multiply this by 3.
1/3 times 3 equals....
1

0.333333333333333........... times 3 equals...
0.999999999999999............

But wait! It should be 1 ! Why?
Because 1/3 and 0.33333... are equal. Times three, they both should equal one.
So that means 0.999999..... is actually 1 !

Now back to the first part. Why does infinity times 0 = 1?
This is because 1-0.999999999999999999999.... = 0
(remember, 0.999999999...... is 1.)
But 1-0.99999....= 0.000......1
This means that 0 and 0.000000......1 are the same.

So if you multiply that tiny 0.000000....1 by infinity, by the power of infinity, it will be 1.













































Hi. James Dai