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

You are not logged in.

#2 Re: Dark Discussions at Cafe Infinity » Brazil 1-7 Germany » 2014-07-14 01:38:34

Germany 1-0 Argentina after extra time. Well done Germany! cool

#3 Dark Discussions at Cafe Infinity » Brazil 1-7 Germany » 2014-07-08 22:43:37

Nehushtan
Replies: 14

Germany – out of this world!

Brazil – out of this World Cup …

20140708Brazil1-7Germany.jpg

#4 Re: Help Me ! » Factoring x^3-3x^2+x=0 » 2014-06-30 00:03:16

That’s all you can do. The quadratic polynomial



is irreducible over
and
.

In a way you could write

but this is probably not what you want.

#5 Re: Help Me ! » Sequences » 2014-06-08 00:44:07

Agnishom wrote:

The series is undefined as the first term is
.

#6 Re: Help Me ! » Inequality? » 2014-06-03 10:28:27

Agnishom wrote:

If a,b,c > 0
and abc=1

Prove that a^2 + b^2 + c^2 ≥ a+b+c


Jensen’s inequality states that if
is a convex function then



The function
is convex; therefore



But
by AM–GM.

Hence

#7 Re: Help Me ! » Number Theory » 2014-05-09 08:07:40

Consider

This is a G.P. with common ratio

so we have

But n is odd so

.

Multiplying both sides by

gives

Since the LHS is an integer, the RHS must be an integer. QED.

#8 Re: Dark Discussions at Cafe Infinity » How has mathematics enriched your life? » 2014-05-07 05:18:27

Mathematics has given me a university degree I can wave in front of everyone to show them how smart I am.

#9 Science HQ » Ununseptium » 2014-05-06 04:00:07

Nehushtan
Replies: 2

The periodic table is set to get a new addition – say hello to the superheavy element ununseptium

http://z8.invisionfree.com/DYK/index.ph … p=22021672

#11 Euler Avenue » Why we have 12 and 60 in our time system » 2014-05-03 01:35:15

Nehushtan
Replies: 2

There are 60 seconds in a minute. There are 60 minutes in an hour. And a day has twenty-four hours – 12 hours of daylight and 12 hours night averaged through the year.

What makes the numbers 12 and 60 so special?

http://z8.invisionfree.com/DYK/index.php?showtopic=976

#12 Re: Help Me ! » Set Theory Identity » 2014-05-02 00:28:45

Agnishom wrote:

Please Tell me how I can show


Note that
is a subset of
. In general, if
then
.

Proof:

We must prove that both

and
.

is clear since
is a subset of
.

To prove the other inclusion, suppose

and let
.
. If
we are done. If
then, since
, we have
as well. In either case
. Hence
.

#13 Re: Help Me ! » Set Theory Identity » 2014-05-01 22:52:50

Agnishom wrote:

Sorry, it is supposed to be This:
Prove that:

That’s better. smile

and it is easy to see that

.

#14 Re: Help Me ! » Set Theory Identity » 2014-05-01 22:31:41

Something is wrong with your question.

#18 Re: Help Me ! » How to solve this? » 2014-04-01 02:12:15

Let’s assume

is 1 or prime. Then it divides 2 or
.

(i)

divides 2
or
or
. So
.

(ii)

divides
. For this to be an integer,
. So
. So
which is the same as (i) above.

So

if
is 1 or prime. There are other solutions if
is not 1 and not prime – but as you are not told to find them all, I think I’ll stop here.

#19 Re: Euler Avenue » Contradictory mathematical terminologies? » 2014-03-30 13:13:10

JaneFairfax wrote:

“Contradictory” is perhaps not a good word to use in the title of this thread. “Oxymoronic” might be better, I believe. It is not contradiction that I wish to explore, but rather oxymoron: http://z8.invisionfree.com/DYK/index.php?showtopic=69 big_smile

If I said that someone was an unpleasant kind of person, I would be uttering an oxymoron.

#22 Re: Puzzles and Games » Easy puzzle challenge » 2014-03-26 00:29:42

Here is another problem for all the brainy people here.


#23 Re: Puzzles and Games » Easy puzzle challenge » 2014-03-22 00:13:23

Can I remind everyone that the title of this thread is Easy puzzle challenge. Therefore if your solution is messy and complicated, you’re on the wrong tack.

#24 Re: Help Me ! » Triangles » 2014-03-21 23:52:37

Ah, I knew there had to be a much simpler solution than using coordinates and vectors. Nice work, Bob. smile

Board footer

Powered by FluxBB