I know this is a seriously lame question but i need help!!?

Question

How on earth did Betrand Russel prove that 1+1=2 and wat was its significance??

Answer 1

NOT lame at all. There is a lot of math and philosophy in the two connected questions here - what is the logic behind the statement and how do you prove it.

Basically, if we can prove the 1+1=2, we can construct all the natural, real, etc numbers.

See the first two sets of references below for a more understandable explanation of the significance of these questions / equation.

Sorry, the previous answers don't quit explain clearly; and I may not either but here goes (and it is really late here and now).

The following are the main points (I diverge slightly from the standard definitions):

> the number of items in a set can be represented by an ordinal number,
> there is a set with no elements called the empty set that has '0' as its number
> to do it right, it gets a little tricky with the definition of a 'successor' number - for common talk, pick a number and the successor is that number which comes next
(see http://mathforum.org/library/drmath/view/61208.html)
> finally, we can define "addition" by either 'taking the successor' or by the' operation' of adding 1 and therefore make the nontrivial statement that 0 is not equal to 1 (or 1 is not equal to 2), see Peano article and the reference above

Overall, the logic is that there is
> a set that has nothing in it (called/represented by 'zero' )
> there is another set with 1 item (represented by the number / symbol1)
> these numbers are not equal, so
> we can create *all* the numbers by using various rules or operations (one of which is named 'successor,' another is named the operation of adding '1,' and there are others like multiplication, etc)

phew, clear as mud, see the mathforum references.

Answer 2

It took two great mathematicians - not just Russell, but Whitehead as well - to establish the proof, and when they did, they ended up commenting that "from this proposition it will follow, when arithmetical addition is defined, that 1+1=2"

In other words, they didn't prove 1+1=2. They just laid the groundwork for it.

It's on page 379 of volume 1 of Principia Mathematica.

And although I have a bachelor's degree in mathematics, I have to admit that this is pretty heavy slogging for me.

They actually completed the proof in the second volume, page 86, where he makes the comment, "The above proposition is occasionally useful."

The significance lies mostly in the fact that Bertrand Russell and Alfred Lord Whitehead created much of the groundwork for symbolic logic. This was one of the 25 most important books of the 20th century!

Answer 3

It took two math genuses, not just Russell, but Whitehead as well, to establish the proof, and when they did, they ended up commenting that from this proposition it will follow, when arithmetical addition is defined, that 1+1=2

Answer 4

YES. the proof contains lot of logic knowledge. you can find from the book Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.
written by betrand russell page no 378.
http://quod.lib.umich.edu/cgi/t/text/pageviewer-idx?c=umhistmath;cc=umhistmath;rgn=full%20text;idno=AAT3201.0001.001;didno=AAT3201.0001.001;view=pdf;seq=00000400
you can also refer a simple proof of 2+2 = 4 (not same as 1+1=2) in this following link.
http://us.metamath.org/mpegif/2p2e4.html
for this you should be thorough in mathematical logic.

Answer 5

Read all about him on the link provided below.