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#2 Re: Help Me ! » [ASK] How to Read A'? » 2019-03-25 22:02:39

Monox D. I-Fly wrote:

And here I thought that A' in the context of sets meant the complement of A.

It can indeed -- the notation can be quite varied!

#3 Re: Help Me ! » [ASK] How to Read A'? » 2019-03-24 21:51:02

A' is read as 'A dash' in British English and 'A prime' in American English, although at my university 'A prime' was far more common, probably due to American influence.

In Littlewood's Miscellany, Littlewood jokes about this notation used in the context of sets (in point-set topology, A' is the set of all limit points of A, so that A' is called the derived set of A).

John E. Littlewood wrote:

I have had occasion to read aloud the phrase "where E' is any dashed (i.e. derived) set". It is necessary to place the stress with care.

#4 Re: Exercises » Number of integer solutions » 2019-02-24 05:31:26

Hi Amartyanil,

Yes: try looking at that equation modulo 2 and modulo 3. From there you can deduce that x is a multiple of 2 and that y is a multiple of 3, which allows you to reduce that equation into something much simpler!

#6 Re: Help Me ! » Integration » 2019-01-26 06:28:43

Hi Math 1122,

Welcome! Why not register an account with us?

You can start by using the identity

You'll also need (some, if not all of) these facts:

#7 Re: Exercises » Integration » 2019-01-25 11:16:35

Hi Bob,

I made a video explanation here, if Zeeshan 01 would like to have a look. smile

https://youtu.be/IwmYetE29YU

#8 Re: Exercises » Integration » 2019-01-18 03:03:53

Set

then use the trig identity

#9 Re: Help Me ! » Express ∛(7 + 5√2) in the form x + y√2 » 2019-01-10 07:39:45

Hi segfault,

Welcome to the forum!

Suppose that there are some values x and y for which ∛(7 + 5√2) = x + y√2. What happens if you cube both sides of that equation?

#12 Re: Exercises » Formula » 2018-11-29 03:12:42

What is
?

How can you use this to determine
?

#13 Re: Help Me ! » Number Properties » 2018-11-15 22:26:31

and
is sufficient to generate all three.

#14 Re: Help Me ! » Quasilinear 2nd order PDEs with inital data » 2018-10-29 22:32:14

Hi Emma22,

Welcome to the forum. Have you considered registering an account with us?

Emma22 wrote:

The general solution obtained is u(x,t) =F(x^2-t^2*exp(u)) and the initial condition is u(x,0)=2ln(x)

What is
here? (You have later called this
.)

#15 Re: This is Cool » Repeated cosine converges! » 2018-10-10 01:34:18

Hi Βεν,

Nice contribution! Yes, the repeated iteration of the cosine function converges: actually, it converges to the fixed point of the cosine function, i.e. the solution to
. (I think the two different answers come from using degrees versus radians rather than real vs imaginary.) There are ways of calculating this in terms of the Lambert W function or some nice infinite sums of Bessel functions I think.

You can prove that a solution to the above equation exists via Brouwer's fixed point theorem (and probably the contraction mapping theorem too).

#17 Re: This is Cool » Something ineteresting » 2018-10-10 00:33:14

Βεν Γ. Κυθισ wrote:

it should be (a^m)n^a.

Do you mean
rather than
?

#18 Re: This is Cool » Something ineteresting » 2018-10-09 23:34:30

Hi Βεν,

Welcome to the forum! Thanks for your contribution. That looks like a nice list. Some comments:

a^n=a multiplied by itself n times

I know what you mean, but this can be misleading:
is multiplied by itself
times. For example,
, where
gets multiplied by itself one time.

If n is even then (-a^n)=a^n

The brackets should go around the
here, i.e.
for even
.

a^n÷a^m=a^(m-n) (Makes sense right?)

On one side of the equation, the
and
are the wrong way round. It should read:

If n>0 then (a^m)na=a^(m+n)

What did you mean here?

#19 Re: Euler Avenue » Sine and cosine » 2018-10-03 01:13:18

Hi zahlenspieler,

I have fixed your LaTeX.

#20 Re: Help Me ! » Algebra: Polynomial Question » 2018-10-01 01:12:02

Hi math9maniac,

Can I just check that the equation you wrote down is correct?

#22 Re: Help Me ! » Exponential expression » 2018-09-28 22:32:53

OK, suppose we had
. Then:

In this case, we have
. We want to calculate
, which means we need to multiply the index (
) by
. Can you see how to do this?

#23 Re: Help Me ! » Exponential expression » 2018-09-28 21:14:39

Hi vipin_sharma,

Welcome to the forum. Here's a hint:

#24 Re: Help Me ! » answer for this series: 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 1 » 2018-09-23 05:52:10

Hi niravashah,

Thanks for posting this. Have you considered creating an account with us?

For reference, the sequence is:

4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6,

and we're asked to find the next two terms. Perhaps this will give you a hint:

4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6,

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