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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#2 Re: Help Me ! » Limits » Yesterday 21:11:20

I don't think 1 is correct. Have you tried to plot it. It's wild.

#3 Re: Help Me ! » Limits » Yesterday 13:04:55

I don't think it exists.

#4 Re: Help Me ! » Limits » 2014-11-20 12:36:51

Where did he not allow the squeeze theorem?

#5 Re: Help Me ! » Limits » 2014-11-20 11:13:03

You can divide both the denominator and the numerator by x, then use the known limits of sin(x)/x and tan(x)/x.

#7 Re: Maths Is Fun - Suggestions and Comments » Set Symbols » 2014-11-17 17:02:23

Hi MIF

Not sure if that's the general case, but I've seen the bolded "I" be used mostly for irrational numbers.

#8 Re: Dark Discussions at Cafe Infinity » Dihydrogen Monoxide » 2014-11-14 11:14:14

I heard it was used a long time ago by the primitive native tribes of San Serriffe.

#10 Re: Help Me ! » Is there such a function? » 2014-11-12 12:26:28

Yep. Here's another interesting one:

Does continuity of a function f on [a,b] guarantee continuity of the function g(x)=sup{f(t)|a≤t≤x} on [a,b]? What about differentiability?

#12 Re: Help Me ! » Is there such a function? » 2014-11-12 06:22:53

It can, why do you think it can't?

#14 Re: Help Me ! » Is there such a function? » 2014-11-12 05:13:53

Well, it certainly does exist.

Think of it this way: If you take any number that's a period, there is a number smaller than that one that's also a period.

#15 Re: Help Me ! » Is there such a function? » 2014-11-12 04:21:44

It is, but can you find such a function?

#16 Re: Help Me ! » Is there such a function? » 2014-11-12 03:31:05

Smallest means exactly what you think it would mean. I don't think there is any ambiguity there.

Well, every periodic function has infinitely many periods.

#17 Re: Help Me ! » Is there such a function? » 2014-11-12 02:41:03

Hm, but that function would not be periodic.

#18 Re: Help Me ! » Is there such a function? » 2014-11-11 22:35:16

Well, as it was shown that no function can have uncountable extrema, the Weierstrass function cannot have uncountable extrema.

Fixed post 59:

anonimnystefy wrote:

Speaking of which, here is a question.

Does every non-constant periodic function have a smallest positive period?

#19 Re: Help Me ! » Is there such a function? » 2014-11-11 21:01:18

It is not periodic, so it does not have a period.

#20 Re: Help Me ! » Is there such a function? » 2014-11-11 19:04:26

Speaking of which, here is a question.

Does every non-constant periodic function have a smallest positive period?

#21 Re: Help Me ! » Is there such a function? » 2014-11-11 02:33:20

Well, each of those intervals has rational endpoints, so there are certainly countably many.

#22 Re: Help Me ! » Is there such a function? » 2014-11-11 02:04:02

It's more likely in Serbian, but that's not important. The book is in English.

#24 Re: Help Me ! » Is there such a function? » 2014-11-10 08:18:20

I asked a professor today about this problem and also found out the answer to your question.

It's needed to be shown that each of those extreme points can be isolated inside an interval so that no two intervals intersect.

#25 Re: Help Me ! » Is there such a function? » 2014-11-09 05:16:18

I don't think there are uncountably many peaks, but I'm not sure.

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