0 and 1 in exponents
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
.
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1 solution
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. :-)
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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
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We were featuring your problem, and decided to add more explanation / clarity to your statements. Thanks for adding in more details :)
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. ;)
Haha, did thw naughty staff play a role in this XD
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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
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@Hung Woei Neoh – That is true but did you understand who I was referring to as naughty staff :P
Uno elevado a infinito es indeterminado.
One raised to infinity is undetermined.
1⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹⁹......................infinite..............................⁹⁹⁹⁹⁹ is undetermined.
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If I remember correctly, all real values of x meant:
− ∞ < x < ∞ or ( − ∞ , ∞ )
It does not include infinity
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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.
I think this question is good :)
Edit your second statement please , It is x 1 = 1 And not x 1 = x
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Hmm? I asked how many statements were correct, right?
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
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I've added the clarifying statement of "Here are what the corrected statements should say:" to your solution.
Relevant wiki: Rules of Exponents - Algebraic
Only 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 = 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 = 0 1 = Undefined = 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