Happy Birthday Euler

[d000hg]

They are an abstract notation invented by man, unless you can show me an actual integer?

Pi exists as the half ratio of the radius to circumference of a circle in Euclidean space regardless if we know about it. A circle exists as a 2D shape even if we haven't invented it... a circle is a mathematical construct but it still exists whether or not people know about it.

[proggy]

Pi exists as the half ratio of the radius to circumference of a circle in Euclidean space regardless if we know about it. A circle exists as a 2D shape even if we haven't invented it... a circle is a mathematical construct but it still exists whether or not people know about it.

PI is not an integer neither is a circle, perhaps a elementary course is required?

[d000hg]

<adds proggy to ignore list as just another soon-to-be-banned sockie incarnation>

Bye proggy. Catch you next time you're perma banned.

[proggy]

<adds proggy to ignore list as just another soon-to-be-banned sockie incarnation>

Bye proggy. Catch you next time you're perma banned.

Wow such a bad loser.

[sasguru]

<adds proggy to ignore list as just another soon-to-be-banned sockie incarnation>

Bye proggy. Catch you next time you're perma banned.

Bit of a shame you couldn't argue with his point. And you insulted him first to be fair.
As I've mentioned before your hypocrisy is glaring.

[EternalOptimist]

It's true that there are a million ideas out there that are yet to be discovered, or articulated.

If there were no people, there would be an awful lot more, obv.

Once an idea is articulated and becomes common currency, it's almost impossible to imagine life without it. Most peoples reaction is 'well, I could have thought of that'
but they didn't , and they can't. mostly

[d000hg]

Bit of a shame you couldn't argue with his point.

I did. He said integers weren't 'real', I countered by mentioning other things which aren't 'real' either but exist. He said those weren't integers so it didn't count - anyone who can't follow such a simple thread of argument clearly isn't able to understand. It would be like trying to educate a bible-belter about quantum physics.

[sasguru]

I did. He said integers weren't 'real', I countered by mentioning other things which aren't 'real' either but exist. He said those weren't integers so it didn't count - anyone who can't follow such a simple thread of argument clearly isn't able to understand. It would be like trying to educate a bible-belter about quantum physics.

LIke all Christians you're an expert in avoiding the obvious: you've had plenty of practice.

You were talking about integers and you got shown up.

Talking about the non-integer constants: as I pointed out to NAT, there is a case for arguing that the non-integer constants are in some sense more "natural" than the integers.

So yes I think proggy had you by the balls.
If you'd like to clear your mushy brain on this point try reading "Number" by Tobias Dantzig.

[d000hg]

You were talking about integers and you got shown up.

Sorry Sas since your post isn't an integer it doesn't prove anything.

Shall I assume proggy is your sockie? Are you also claiming integers are invented rather than discovered?

[NotAllThere]

Parroting Kronecker's dictum without reflecting on how e and pi are so ubiqitious in nature, and hence would be "God's constants" explains why you have just read Spivak and not done the exercises* (wherein lies the meat).

*And if you claim to have done them and found them easy, I'll call you a liar.

PS if anyone is inspired to learn more on Euler try Dunham's "Euler:Master of us all".

Given that Spivak was my course book for Real Analysis, and I got a first in the subject (in 1989, before the great dumbing down of degrees), I guess you'll just have to call me a liar.

Imagine how much that bothers me.