# Math Is Fun Forum

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

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## #1 Re: Help Me ! » Simplify Expression...3 » 2024-05-16 19:17:36

The solution is correct, but I'd do it like this:

## #4 Re: Help Me ! » Number "Closest" to Zero » 2024-05-14 09:13:03

Bob wrote:

No.

Suppose n was the number. Let's say its decimal form is 0.00000...x...... Let x be the first non zero digit. There must be such a digit or else the number is zero.  And say the next digits are y and z.

ie. n = 0.00000...xyz...... where every digit before x is zero.  Change x to zero too. New number is 0.00000.....0yz....... so it's smaller. So the number we thought we'd found isn't the smallest.

Bob

Sure, this does work if the number is non-terminating, but what about a situation like this:
Let's suppose n is in the form x × 10^-p, where x and p are counting numbers. For example, let's suppose n = 125 × 10^-6 = 0.000125.
Let's make a sequence S where S₁ = n, and S_{z+1} is S_z but with the first non-zero digit replaced with 0.
Then, the sequence will go like this:

S_1 = 0.000125
S_2 = 0.000025
S_3 = 0.000005
S_4 = 0.000000 (not positive)

So we can see that this doesn't work all the time.

Let's make another sequence T, where T₁ = n, and T_{z+1} is T_z / 2. Here's how it goes now:

T_1 = 0.000 125
T_2 = 0.000 0625
T_3 = 0.000 03125
T_4 = 0.000 015625
...

Let's try it with a non-terminating number:

T_1 = 0.000 333333...
T_2 = 0.000 166666...
T_3 = 0.000 083333...
T_4 = 0.000 041666...
...

So halving does work all the time.

## #5 Re: Help Me ! » Trains to Coney Island » 2024-05-14 08:54:08

Sorry for the mistake, I fixed it.

## #6 Re: Exercises » 5 problems » 2024-05-14 08:50:47

KerimF, use the hide tag if you don't want to straight-up reveal the answer.

## #7 Re: Help Me ! » Trains to Coney Island » 2024-05-14 00:06:40

Remember: you can use the hide tag to make your answer hidden in a button.

Hi Jai,

Hi,

## #10 Re: Puzzles and Games » Zeros not allowed! » 2024-04-27 21:51:59

As you say, Irene.

## #11 Re: Help Me ! » LaTeX - A Crash Course » 2024-04-27 21:42:24

To not get italicized text, use the \text{} tag.

area \ of \ a \ circle = \pi{r^2}

gives

but

\text{area of a circle} = \pi{r^2}

gives

## #12 Re: Exercises » Compute the solution: » 2024-04-27 21:37:16

Wait, wouldn't it be "Find that number"?

## #13 Re: Introductions » hello everyone!!! » 2024-04-27 21:28:55

Hello, MathAppreciator,

Welcome to the forum

## #14 Re: Exercises » isosceles right-angled triangle » 2024-04-05 23:43:34

You can put a backslash before the "sin" for it not to display italic.
If it was italic, sin(x) would really mean s×i×n×x.

Hi,

Hi,

Hi,

## #18 Re: Introductions » A solo scientist new to the forum » 2024-04-02 09:13:03

Hi Opichem,

Welcome to the MIF forum!

Hi,

## #20 Re: Help Me ! » Numbers - Hierarchy » 2024-04-01 09:14:57

The study of big numbers is also called "googology".

## #22 Re: Puzzles and Games » I have created a daily number puzzle game » 2024-03-24 05:45:01

There are already dozens of variations of Wordle. One of them is Nerdle, which is based on math.

## #24 Re: This is Cool » Hilbert's paradox of the Grand Hotel » 2024-03-13 03:23:17

It is also possible to accommodate an infinite amount of infinitely many guests, like if you had infinitely many buses with infinitely many guests in each:

**|01 02 03 04 05 ...
--+------------------
01|01 02 06 07 15 ...
02|03 05 08 14 16 ...
03|04 09 13 17 25 ...
04|10 12 18 24 30 ...
05|11 19 23 31 39 ...
..|.. .. .. .. .. ...

## #25 Re: Exercises » Compute the solution: » 2024-02-13 05:52:56

Hello, can anyone tell me how to put a message inside a button?