SRL Archive - Discussions & Debates

e
a! is always an integer as long as a is an integer. "!" can only be used with integers, so a must be an integer.
1/a is a rational number as long as a a rational number. Formerly we prooved that a is an integer and a rational number.
The sum of n rational numbers is always rational.
Thus e is rational.

Pi
All functions have integral functions. That means that
also has an integral function, F. Thus you can calculate F(1) - F(0), which of course has some accurate value.
The proof of Pi's transcedentality (??) is based on the fact that e is transcendental, which I don't find reliable fact at all.

Discuss?

Once I get to the ∞th decimal of e it'll end :)

That's essentially what you're saying, since you're taking a sum of infinite rational numbers, for which you can never have it end

"The sum of n rational numbers is always rational."

not always true if its an infinate sum.

From: Yakman
"The sum of n rational numbers is always rational."

not always true if its an infinate sum.

I know that, but if you think of it it doesn't make sense. That's an exception we have to apply because we can't handle infinity other way. Infinite sum is a sum like any other. It's like limit values:
This function never gets value 1, it's just the value if gets closer and closer as x increments. Talking about infinity is actually talking about limitvalues in most cases. That can be very distracting. (1/∞) = 0, yet (1/x) = 0 = false.

All this math crap is pretty annoying.

From: marpis
I know that, but if you think of it it doesn't make sense. That's an exception we have to apply because we can't handle infinity other way. Infinite sum is a sum like any other. It's like limit values:
This function never gets value 1, it's just the value if gets closer and closer as x increments. Talking about infinity is actually talking about limitvalues in most cases. That can be very distracting. (1/∞) = 0, yet (1/x) = 0 = false.

lim_x->0 (x+1)/(x) == lim_x->0 (1)/(1) because of l'Hospitals rule.

You proved nothing new..

From: marpis
e
a! is always an integer as long as a is an integer. "!" can only be used with integers, so a must be an integer.
1/a is a rational number as long as a a rational number. Formerly we prooved that a is an integer and a rational number.
The sum of n rational numbers is always rational.
Thus e is rational.

Pi
All functions have integral functions. That means that
also has an integral function, F. Thus you can calculate F(1) - F(0), which of course has some accurate value.
The proof of Pi's transcedentality (??) is based on the fact that e is transcendental, which I don't find reliable fact at all.

Discuss?

e is rational? Awesome :p You have to note that the basic formula for the limiting sum is not entirely accurate.

S = a(1 - r^n)/(1 - r)

When r < 1 and n is infinity, S = a(1 - [tiny value])/(1 - r), not necessarily a/(1 - r).

This just proves that the limiting sum really is a limiting sum, and not an accurate value. I'm quite sure something similar applies here, can't be sure though.

As for the proof of irrationality of Pi:


Now F(1) involves the inverse sine function of 1, which is Pi/2. Therefore your claim that F(1) is a rational value is invalid, because it is based around the assumption that Pi/2 is rational…when the whole point is to prove this and not assume it.