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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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.
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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