relative complements

[AntonioLao]

For the universal set U and subsets A, B of U, the following three identities are always true:

1. A – A = O
2. O – A = O
3. A – U = O

Here, O is known as the empty set.

[mkirkpatrick]

For the universal set U and subsets A, B of U, the following three identities are always true:

1. A – A = O
2. O – A = O
3. A – U = O

Here, O is known as the empty set.

Surely Antonio 0 is always empty,thats why it is set at zero!


regards michael.

[AntonioLao]

0 is always empty,thats why it is set at zero!

What could then be the absolute complement of the empty set 0? Is it complement to itself?

[mkirkpatrick]

What could then be the absolute complement of the empty set 0? Is it complement to itself?

No it does not,it leaves that task to us?

regards michael.

[Guille]

For the universal set U and subsets A, B of U, the following three identities are always true:

1. A – A = O
2. O – A = O
3. A – U = O

Here, O is known as the empty set.

Spanding 2, we get A-A-A=O=A-A but that is like saying -2=0. Or is arithmetic logic broken in this set theory?

I like seeing everything as part of other areas to which they are not supposed to belong. So, we could say that 3 explains that an individual without a society is nothing. What is then U-A=?

[AntonioLao]

that is like saying -2=0

This is a way to show that the entire universe is empty even though there are matter and energy.

What is then U-A=?

The universe minus matter is just energy --- Universe - Matter = Energy or Universe - Energy = Matter.

[Guille]

The universe minus matter is just energy --- Universe - Matter = Energy or Universe - Energy = Matter.

So, matter and energy are inverses of each other?

Also, if Matter+Energy = Universe, what is the place of Force?

[AntonioLao]

So, matter and energy are inverses of each other? Also, if Matter+Energy = Universe, what is the place of Force?

I go with Einstein's E = mc2. Force is found within energy. There are different forces for different types of energy.

[mkirkpatrick]

I go with Einstein's E = mc2. Force is found within energy. There are different forces for different types of energy.

What would yousay Antonio,is the difference,if any,between energy and force,and say power?
The reason I ask this Antonio is because I see only one energy within this universe,and
not many,so are forces aspects of energy,or something different?


regards michael.

[AntonioLao]

the difference,if any,between energy and force

Energy is the measure of change. Force is the agent of change. These definitions were taken from one advanced placement physics review book.