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[J a c k]

Welcome.

Now to business. Kudos are a sort of “like” or thumbs up. Reps are given to express appreciation of a member’s quality, per se. The etiquette here is that you must rep J A C K as soon as possible in order for you to be taken seriously. You’re welcome.

[The Valkyrie]

Welcome.

Now to business. Kudos are a sort of “like” or thumbs up. Reps are given to express appreciation of a member’s quality, per se. The etiquette here is that you must rep J A C K as soon as possible in order for you to be taken seriously. You’re welcome.

If you don't give a rep to Jack, she gets depressed.

Then she drinks.

Then she gets angry.

And you don't want Jack angry with you.

[J a c k]

Welcome.

Now to business. Kudos are a sort of “like” or thumbs up. Reps are given to express appreciation of a member’s quality, per se. The etiquette here is that you must rep J A C K as soon as possible in order for you to be taken seriously. You’re welcome.

If you don't give a rep to Jack, she gets depressed.

Then she drinks.

Then she gets angry.

And you don't want Jack angry with you.

You are correct. I know a crazy lady with a scalpel and I’m not afraid to use her!

[The Valkyrie]

If you don't give a rep to Jack, she gets depressed.

Then she drinks.

Then she gets angry.

And you don't want Jack angry with you.

You are correct. I know a crazy lady with a scalpel and I’m not afraid to use her!

So you keep promising.

[polymath257]

Most of my research has related to various aspects of harmonic or functional analysis.

I wasn't expecting the Spanish Inquisition!

Come on guys, it took until page 6 for someone to reply properly? When he set us up so perfectly? I'm ashamed in you all.

Welcome to the forum polymath! I love math, haven't studied beyond intro calculus so far though. What's your view on using approximations in calculations (ex. pi = 3)?

It depends on what you are calculating and why. For example, if the irrationality of the number is important, using pi=3 would be a very idea. If, instead, you want to get an order of magnitude estimate for some physical process, it would be useful.

The point is that pi is NOT the same as 3 or 22/7 or 355/113. It is an irrational number. It is even a transcendental number (not the root of any polynomial with integer coefficients). There are cases where this is an important aspect of the number pi.

But, for example, we do not know whether pi+e is irrational or not. Most mathematicians suspect it is, but nobody has found a proof. There is no way to tell this by an approximation.

[Kernel Sohcahtoa]

Come on guys, it took until page 6 for someone to reply properly? When he set us up so perfectly? I'm ashamed in you all.

Welcome to the forum polymath! I love math, haven't studied beyond intro calculus so far though. What's your view on using approximations in calculations (ex. pi = 3)?

It depends on what you are calculating and why. For example, if the irrationality of the number is important, using pi=3 would be a very idea. If, instead, you want to get an order of magnitude estimate for some physical process, it would be useful.

The point is that pi is NOT the same as 3 or 22/7 or 355/113. It is an irrational number. It is even a transcendental number (not the root of any polynomial with integer coefficients). There are cases where this is an important aspect of the number pi.

But, for example, we do not know whether pi+e is irrational or not. Most mathematicians suspect it is, but nobody has found a proof. There is no way to tell this by an approximation.

Have you attempted to prove this? Has anyone come close?

[polymath257]

It depends on what you are calculating and why. For example, if the irrationality of the number is important, using pi=3 would be a very idea. If, instead, you want to get an order of magnitude estimate for some physical process, it would be useful.

The point is that pi is NOT the same as 3 or 22/7 or 355/113. It is an irrational number. It is even a transcendental number (not the root of any polynomial with integer coefficients). There are cases where this is an important aspect of the number pi.

But, for example, we do not know whether pi+e is irrational or not. Most mathematicians suspect it is, but nobody has found a proof. There is no way to tell this by an approximation.

Have you attempted to prove this? Has anyone come close?

Well, there is a conjecture due to Lang that given any real numbers x_1 ,...x_n, then the transcendence degree of Q(x_1 ,...x_n, e^{x_1},...e^{x_n}) is at least n. This would give the transcendence of e+pi, but nobody has a proof of this conjecture either.

There are some pretty remarkable results in transcendence theory. It isn't my area of specialty, so I haven't seriously attempted proofs in the area, The issue seems to be the addition of exponentials and logarithms (recall that i*pi is a logarithm of -1).

All transcendence proofs that have been discovered so far are done via contradiction (not surprising given the definitions involved) and amount to getting a contradiction by finding an integer between 0 and 1 using sophisticated approximation techniques.

A very easy example of a transcendental number is the sum of 1/10^(n!). The proof shows it can be approximated by rationals too well to be algebraic!