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#1 Help Me ! » Function Series and Continuity? » 2011-11-26 05:15:44

Replies: 0

So, we have

I want to show that it is continuous on the real numbers, but I have no idea what to do. I obviously thoguht of using Weierstrass's M-test, but even if I got that to work, it would only show that g is uniformly convergent. Is there anyway to use uniform convergence to show that g is continuous? Or, am I just headed in the complete wrong direction?

#2 Help Me ! » Bijection between an open and half closed interval? » 2011-10-04 01:27:59

Replies: 1

I'm doing this math puzzle sheet that my teacher has given me for fun to prep for the putnam, and I can't quite figure this one out. It's supposedly one of the easier questions, but it still hurts my head.

It wants me to find a bijection h: (0,1)->[1,3).

Any ideas?

#3 Help Me ! » Probability » 2011-01-17 16:05:30

Replies: 4

Ok, I have a question that I just cannot figure out.

I want to find out how many five letter strings I can make if none of the letters are the same. The string must also be in alphabetical order.

For example, ABCDE is okay, but ABCED is not.

Can any one help me?

The only real killer part that I can't figure out is the alphabetical order part.

#4 Re: Help Me ! » Number of Factors. » 2009-06-07 19:42:04

Avon wrote:

then it turns out that
is odd, so there can be no solution when a is even.


is not always odd.

For example, let x = 4.

I think that the question is looking for a general solution that works all the time. The solution you provided does work, but only when x+1 is a prime power. There still needs to be a solution for when x+1 is not a prime power.

I think that there may need to be many separate solutions to find the all the possible solutions for this problem, like an expression for x when a is odd and a different one when a is even. The question states that b needs to be odd and a can be anything as long as both a and b are integers greater than ten and less than 99.

#5 Re: Help Me ! » Number of Factors. » 2009-06-07 13:15:35

I don't mean to be rude, but I reread the question and it does say that b is odd.

Also, I may be wrong, and if I am please tell me, but I am not sure if that solution works all the time. What if (x+1) is not a prime power?

#6 Re: Dark Discussions at Cafe Infinity » Haikus » 2009-06-07 10:18:02

Leaders climb up ladders
Go high and unreachable
Empty paws return

#7 Re: Help Me ! » Number of Factors. » 2009-06-07 10:14:39

Can no one help me with this? This problem has been bugging me for a few months now and I still can't figure it out.

#8 Help Me ! » Number of Factors. » 2009-06-05 04:25:12

Replies: 10

There is this problem I cannot figure out. There are two parts to it, but I have only figured out one of them.

The notation, "

," signifies the number of factors that N has. For example,
is equal to 3 because it has 3 factors, which are 1,2 and 4.
is equal to 6 because it has 6 factors, which are 1, 2, 3, 4, 6, and 12.

The first part, the one that I could figure out, is as follows:

If b is an even number and both a and b are integers greater than ten but less than 99, find an expression for x using the variables a and b to make the statement above true.

The answer that I found is as follows:

Here is the second part.

If b is an odd number and both a and b are integers greater than ten but less than 99, find an expression for x using the variables a and b to make the statements above true.

I can't quite figure out the last part. Can anyone please help me?

#9 Help Me ! » Log » 2009-02-10 08:15:00

Replies: 3

Why is the base of a log always positive?
We always see

Why do we never see

#10 Help Me ! » Sum of an infinite series. » 2008-10-08 03:35:04

Replies: 1

I am having trouble with this problem.

Find the sum of the infinite series.

I found the solution using teh formula


But, is there a way to put it into sigma notation?

#12 Help Me ! » Inequalities and negative numbers? » 2008-10-07 04:17:59

Replies: 3

I am having trouble with an inequalities problem.

I found the solution to be

, but the real solution is

Why is that? Is there some sort of rule that I do not know about? does it have somethign to do witht eh variable being in the denominator?

#13 Jokes » Pirates. » 2008-10-06 12:11:38

Replies: 2

This is a little joke that I had gotten from a book.

There was once a pirate ship with 138 men on it.

On the very first day at sea, the pirates ran into 8 ships.

The captain commanded, "GRAB ME RED SHIRT!"

The pirates won the battle.

On the third day, the pirates were up against 3 ships.

The captain screamed, "GRAB MY RED SHIRT!"

The pirates lost this battle.

On the eighth day of the voyage, one of the crew members asked, "Captain, why do you always yell for your red shirt before a battle?"

The captain retorted, "It is because if I am ever wounded in battle, my crew won't lose hope."

"Well, that's mighty noble of you captain."

12 days later, the pirates ran into 98 pirate ships.

The captain shouted, "GRAB MY BROWN PANTS!"

#14 Re: Dark Discussions at Cafe Infinity » Hosepipe » 2007-12-02 03:17:09

mason777 wrote:

that makes no sence space is galaxie after galaxie star after star planet after planet (why do you think its called space) God made space no doubt about it

It is impossible to verify that "space is galaxie after galaxie star after star planet after planet."

Not everything has the characteristics that its name implies, such as "space," "pencil LEAD," "koala BEAR", and "mince MEAT pie." Just because it is called "space" does not mean anything at all.

It is also impossible to verify that "God made space," and there is "doubt about it."

#15 Re: Dark Discussions at Cafe Infinity » i dislike people » 2007-12-02 02:58:26

mikau wrote:
JaneFairfax wrote:
Devantè wrote:





mathsyperson wrote:

If someone continues this then Devantè will die.

I don't think that  Devantè should be the one who gets struck by the bolt of lightning. I think that all those other people who started and continued the chain should be sent hang gliding during a thunderstorm. Although Devantè was the one who started the chain, he had no intention of doing that on his first post. WHO WANTS TO GO HANG GLIDING WITH ME!!!

#17 Re: This is Cool » Times 4 Kidz » 2007-11-05 11:32:43

JaneFairfax wrote:

Hey, look. I have a new way of adding two numbers. To add two numbers, you simply follow these steps:

(i) multiply the two numbers
(ii) multiply the predecessors of the two numbers
(ii) subtract the second result from the first result
(iv) add 1

Example, to add 12 + 34:

(i) multiply the numbers: 12 × 34 = 408
(ii) multiply their predecessors: 11 × 33 = 363
(ii) subtract: 408 − 363 = 45
(iv) add 1: 45 + 1 = 46

Hence 12 + 34 = 46.

BUT … is it worth it? Why don't we just add 12 + 34 directly?

Precisely! neutral

Did i do something wrong?

a + b = (a x b) - ((a-1)(b-1)) +1
a + b = (a x b) - (ab - b - a +1 )+1
a + b = ab - ab - b - a +2
a + b = -b - a +2

Did i do something wrong?

#18 Re: Dark Discussions at Cafe Infinity » Hosepipe » 2007-10-30 13:04:41

landof+ wrote:
shocamefromebay wrote:
Devantè wrote:

Can you prove that we all have superpowers?

what defines super powers?

Devantè wrote:

What defines those who define what defines superpowers?

Actually, it all depends on the benchmark, mainly, the border of the two natural orders. If a super dumb alien were to interact with us, it would consider us as 'supernatural' in their language, and in the sense that we are more advanced than them 'naturally' in both languages. dizzy

well actually i believe that supernatural doesn't exist.
this is b/c super natural means beyond what is natural
and what is beyond natural??
i cant think of anything that is beyond natural that also exists...

#19 Re: Dark Discussions at Cafe Infinity » Hosepipe » 2007-10-14 11:22:12

espeon wrote:

lol... I just said... It cant be a hosepipe cause otherwise the imense heat would of melted the rubber XD which is why we dont get gigantic blobs of rubber.. but! it might be rain thats the water from the leaks XD

or maybe the hose pipe is so huge that the heat cant reach it to melt it
or taht the water in the hose pipe keeps it from melting

#20 Dark Discussions at Cafe Infinity » Brain Transplants » 2007-10-06 09:24:05

Replies: 1

Brain Transplants
Can you guys believe this?
Is it true?
How awesome is this?
How far can we get with science?
It really is amazing.
Or is this crossing the line (like stem cell research)?

#21 Re: Dark Discussions at Cafe Infinity » Hosepipe » 2007-10-06 09:20:21

Devantè wrote:

Can you prove that we all have superpowers?

what defines super powers?

#22 Re: Dark Discussions at Cafe Infinity » Wikipedia 2 Million Articles » 2007-10-06 09:19:02

ganesh wrote:

Nice link, shocamefromebay!

i really wonder how wikipedia people make money
i dont find any ads on their articles
and they have TONS of articles
and so many other things on it
i really wonder where they get their paychecks from

#23 Re: Dark Discussions at Cafe Infinity » Hosepipe » 2007-10-06 09:14:32

proving thigns drags all the fun out of life
life would be so much more fun if people published ideas, even if they are exrtemely flawed, just to give that person teh cradit of being creative
and it would also inspire others to be a lot more creaitve also
and besides
proving things is so flawaed
nothing in science can be proven
it can only be not disproven by lots and lots and lots of attempts to do so

#25 Re: Dark Discussions at Cafe Infinity » Wikipedia 2 Million Articles » 2007-10-04 09:10:24

i realy wonder about what really makes an article legitimte (excuse my spelling) for wikipedia
i mean
there are those ppl who post biographies of themselvs
which is kinda not awesome
but what really makes an artcle legit???
there was once an artice that i found that was of an organiztion
which was kind of lgit
but it was also very unorganized
but then it got deleted quickly

so back to my first question

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