psst. rasch.

2 L's in his name.

We did this in our first year Analysis course actually, it was terribly tedious but not too bad all in all.

Try proving that the square root of two exists - now THAT was hell.

I think it took 12 hours of lectures to show it existed and was between 1 and 2 in value.

Give me a calculator and in 2 seconds and I could have told you that.

I'll give you a calculator that doesn't have a square root button. Have at it, Mr. Smartypants.
>> ^jimnms:
Give me a calculator and in 2 seconds I could have told you that.

Call me a simpleton but 1 apple + 1 apple = 2 apples.
I don't need math and a formula that no one understands to prove to me what my brain interprets automatically. I know math is an amazing tool and can be used to compute amazing things but...

Awe crap..., never mind - on to the next video...

The point is not to prove something we all know is correct. The point is to show that it is possible to prove something we all know is correct. Because if that is possible, then proofs of much more complex and useful relations become available to us.

>> ^Sagemind:
Call me a simpleton but 1 apple + 1 apple = 2 apples.
I don't need math and a formula that no one understands to prove to me what my brain interprets automatically. I know math is an amazing tool and can be used to compute amazing things but...
Awe crap..., never mind - on to the next video...

>> ^thinker247:
I'll give you a calculator that doesn't have a square root button. Have at it, Mr. Smartypants.


Now ok, i couldn't work out exactly what the value was, but i could tell you without thinking for a matter of miliseconds that the square root of 2 was between 1 and 2.... I just worked out in my head that..

1.5x1.5 = 2.25
k, lower it bit by bit and you'll get 2.. I mean if i had a calculator without a square root button, easy as pie..

1.4x1.4 = 1.96
1.45x1.45 = 2.1025
1.425....... and so on and so forth.

Do i win something? Or is this as easy as i thought it was? You learned THIS at university?

Ya, I know..., I just had a headache and my witty-comment-brain wasn't working... Cheers~!

>> ^Ornthoron:
The point is not to prove something we all know is correct. The point is to show that it is possible to prove something we all know is correct. Because if that is possible, then proofs of much more complex and useful relations become available to us.
>> ^Sagemind:
Call me a simpleton but 1 apple + 1 apple = 2 apples.
I don't need math and a formula that no one understands to prove to me what my brain interprets automatically. I know math is an amazing tool and can be used to compute amazing things but...
Awe crap..., never mind - on to the next video...

You still haven't proved that the square root actually exists. Because the square root of 2 is an irrational number, you can repeat this process indefinitely and never get to a decimal number that gives 2 if squared. All you have shown us is that if it exists, it lies between 1 and 2 in value.

>> ^dannym3141: 1.4x1.4 = 1.96
1.45x1.45 = 2.1025
1.425....... and so on and so forth.

Well, that was the original challenge.

Hell, i wasn't aware it was POSSIBLE to run out of decimal places that i could go to. I thought EVENTUALLY i'd get there. Perhaps the sun would have burned out and life on earth lost/moved on by then, and possibly the numbers would get beyond the range of human comprehension, and the scope of "accuracy" would be something i could only argue with god himself, but ...?

I mean, my main aim was to say you could do root 2 using a calculator without having a root button. If you take what i did, feed it into a pc and loop it you'd end up with pretty much a calculator for getting the square root of 2, even if it kept going for a squillion years.

As for proving the exact square root of 2 exists, to be fair, i've not been taught any maths beyond a-level yet. This is all just me working stuff out. It doesn't make sense to me that i could ever run out of decimal places and thus be proved wrong that my method would eventually provide the answer. But there are many things that can only be explained mathematically, so perhaps that is the case afterall.

Edit:
Apparently (and then of course) the square root of 2 is exactly the length of the diagonal of a square with side length 1. How can such a thing not have an exact length?

Danny, it's kind of like Pi. The Square root of 2 and Pi have both been troubling Mathmaticians for a long long long time. They are irrational numbers. You can write logical proofs to show that they should exist, or why the exist, but pinning an exact number on them isn't likely.

http://en.wikipedia.org/wiki/Square_root_of_2

http://en.wikipedia.org/wiki/Pi

Kurt Gödel was the premier logician of the 20th century, not Russell. And I'll fight him about that.

>> ^carrot:
Kurt Gödel was the premier logician of the 20th century, not Russell. And I'll fight him about that.


This!

Now for the next question:

Does 0.999... = 1.0?

This was a long time favorite topic of argument among Blizzard employees and on the World of Warcraft forums for whatever reason.

Neatorama had a neat article on it the other day too: http://www.neatorama.com/2010/03/05/9999999-is-equal-to-1-000000/

The good part of mathematics really begins once you start getting away from the stuff that immediately seems useful.

>> ^Skeeve:
Now for the next question:
Does 0.999... = 1.0?
This was a long time favorite topic of argument among Blizzard employees and on the World of Warcraft forums for whatever reason.
Neatorama had a neat article on it the other day too: http://www.neatorama.com/2010/03/05/9999999-is-equal-to-1-000000/


I'd have to assume that the argument was driven by mathematical illiterates. The proof is simple, taking only a few lines...we spent a whole three minutes on it when I was in the 7th or 8th grade.

Let's see if I can remember it off the top of my head.

Subtract 1 tenth of the value to get rid of the repeating decimal
Add 1 ninth of your new value and you get what you started with, which is 1.

.999... - (1/10) (.999...) = .999... - .0999... = .9
.9 * (10/9) = 1

Overall, that's badly worded, but I think it's fairly obvious when you think about it.

.

>> ^my15minutes:
psst. rasch.
2 L's in his name.


Blertrand Russel?