How many statement(s) below is/are correct?

**
Statement 1
**
:
$1^x = 1$
for all real values of
$x$
.

**
Statement 2
**
:
$x^1 = 1$
for all real values of
$x$
.

**
Statement 3
**
:
$0^x = 0$
for all real values of
$x$
.

**
Statement 4
**
:
$x^0 = 1$
for all real values of
$x$
.

0
1
2
3
4

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Thanks for sharing the problem along with an awesome solution. You've explained all the four statements very clearly. Keep it up.

Special thanks for adding the links into the solution. :-)

Sandeep Bhardwaj
- 5 years, 1 month ago

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The original solution was not like this. As far as I know, at least 2 mods or admins edited my solution, and I further added a bit more after that

Hung Woei Neoh
- 5 years, 1 month ago

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Yeah, I guess that's cool. However, you can learn from the edits made by mods/admins to improve further. Finally the solution looks amusing to me. ;)

Sandeep Bhardwaj
- 5 years, 1 month ago

Haha, did thw naughty staff play a role in this XD

Ashish Menon
- 5 years, 1 month ago

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@Ashish Menon – The original solution only contains the corrected statements. A few edits were made by mods and admins, and I found that the explanation as to why the statements were wrong were insufficient. So I edited them XD

Hung Woei Neoh
- 5 years, 1 month ago

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@Hung Woei Neoh – That is true but did you understand who I was referring to as naughty staff :P

Ashish Menon
- 5 years, 1 month ago

Uno elevado a infinito es indeterminado.

One raised to infinity is undetermined.

1⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹......................infinite..............................⁹⁹⁹⁹⁹ is undetermined.

ma pm
- 5 years, 1 month ago

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If I remember correctly, all real values of $x$ meant:

$-\infty < x < \infty$ or $(-\infty,\infty)$

It does not include infinity

Hung Woei Neoh
- 5 years, 1 month ago

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Can you add "real values" into the problem? You can edit your problem through the menu.

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@Calvin Lin – Ah, right, my mistake. I've edited the problem and solution accordingly. Thanks for notifying.

Hung Woei Neoh
- 5 years, 1 month ago

I think this question is good :)

Ashish Menon
- 5 years, 1 month ago

Edit your second statement please , $\text {It is }x^1=1 \text{ And not } x^1=x$

Sabhrant Sachan
- 5 years, 1 month ago

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Hmm? I asked how many statements were correct, right?

Hung Woei Neoh
- 5 years, 1 month ago

If you were talking about my solution, then you should know that I'm giving out the correction to the false statements.

$x^1 = x$ for all values of $x$ . For example, $2^1=2$ or $3^1=3$

Hung Woei Neoh
- 5 years, 1 month ago

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Relevant wiki: Rules of Exponents - AlgebraicOnly the first statement is correct. It is true that $1^x = 1$ for all real values of $x$ .

Here are what the other statements should have been, and the reasons why they are not true:

2) $x^1 = 1$ only holds true when $x=1$ . Example: If $x=2,\;x^1 = 2^1 = 2 \neq 1$ . The true statement should be

3) $0^x = 0$ does not hold true for any non-positive value of $x$ . Example: $x=-1,\;0^x = 0^{-1} = \dfrac{1}{0} = \text{Undefined} \neq 0$ . The true statement should be

4) $x^0 = 1$ holds true for all real values of $x$ except $x=0$ . The value of $0^0$ is indeterminate. The true statement should be

Here's an interesting article on $0^0$