Inspired by Amed Lolo
x x = 1
True or False: The above equation holds for all real values of x .
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18 solutions
Yes. Never divide by 0. Now is your turn. Why?
How is this not true? Just rephrase statement. X=1x.
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We can only multiply two sides of an equation by a nonzero number to solve the problem. If not, 17 can also equal to 50 since 17×0=50×0.
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The example above is x/x=1, not x/y=1. That's why he put a condition. His statement is true.
0/0 is an indeterminate form. It can have any value. Hence, the answer may or may not be 1.
only if x=0 then it will come to an undefined form otherwise i would stand true everywher
but if we rearrange the equation to say that x=x, then 0=0. That's true isn't? Or is there some rule that I'm forgetting?
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In order to rearrange to x=x, the condition of x not equals 0 must still hold. This is because if x were to be 0, in order to rearrange to the form x=x, you must multiply both sides by 0, which would look like 0 * (0/0) =1 * 0 which would give indeterminate = 0,which is not true ever
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Agreed. Even though the rearranged equation is true, that is not what the question asked. In particular, these two equations have different solution sets. We have to be careful when we multiply by a variable term, and ensure it is not 0.
As an explicit example, if we were asked to solve the equation x = 1 , we cannot "multiply throughout by x to obtain x 2 = x and then conclude that 0 = x 2 − x = x ( x − 1 ) hence the solutions are x = 0 , 1 .
but isnt anything times 0 always 0, even if you are multiplying 0 against an indeterminate? If this is false could you give me the name of the reason why it is.
Also if we don't plug any number in for x before we rearrange the equation you can say that x=x. from that equation isn't that the same question that is being asked originally? If it isn't why can't we?
if x=0, the form is indeterminate and we use l'hospitals rule...which yields ans 1. could you pls explain your answer...?
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Use l'hopital for limits, this question does not involve us taking the limit of x/x, rather; we want the exact value
You are not asked to find the limit of the expression. You are asked if the expression is true for all real x, and in particular, x = 0 .
If x/x :⇔ x^0 then x/x = 1
Division is defined as the inverse of multiplication. Meaning a/b is the solution x of the equation bx=a. Okay so lets make that simple.
a/b=x and multiplying by b a=bx
lets say b=0 here. well you got a problem.
a/b=x a=bx plugging in 0 for b a=0*x a=0
Well if a doesn't equal zero then there isn't a solution to x in the equation a=bx. That is the meaning of undefined. However if a and b both equal zero...
a/b=x a=bx plugging in zero for b a=0 x plugging in 0 for a 0=0 x
can you find a number when multiplied by zero equals zero? I can think of about an infinite amount. When both a and b are equal to zero then the solution is any x. That is the definition of indeterminate and is not the same as undefined. It isn't possible to say it doesn't equal one. You cannot say it does without further analysis, i.e. calculus.
[Further comments removed - Calvin]
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Hi Alexander, please be respectful of the community. I have edited your comment accordingly.
@Alexander George 1)Be careful with your language.
2)It's true that 0=0(x) has infinite solutions,but you have to see if they satisfy the original equation.No solution of 0=0(x) satisfies the original equation because 0/0 is undefined.It isn't equal to anything,because it's not even defined.Therefore you can't say that it is equal to one
3) lim x → a f ( x ) is not necessarily equal to f ( a ) .
Whoa! 14000 solvers!
its a basic any number divisible by zero is equal infinity
But is 0 a real number?
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Yup. Zero is an element of the reals. You may be thinking about the natural numbers, which do not include zero.
0 is a very powerful number. Observe all numbers and find its power. E.g. 01 or 10.
x can not be 0 because 0\0 is undefined so I consider that the answer is 'true'.
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the main thing is that the question said "for all real values of x" and 0 is real and not a solution of x so the answer should be false.
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there are some disscutions about 0 belongs to real numbers; some authors said, that 0 representes absence of amount, so 0 not real; some others said, that 0 represents the "no amount" after the number reaches a level more (from units to tens, for example). But in both cases, 0 is NOT consider a true quantity; yes, zero is necesary but in this case, personally, I can't say that zero belongs to real numbers, so the answer should be true.
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@Carlos Nino – How could you explain the number pf dinosaurs in the planet? It is true some mathematicians say zero does not exist, but it is necesary and that's why they created the natural numbers so that one does not include zero. 0/0 is not de fines so the answer is false
You cannot consider a division by zero, x can never be zero because the equation would not exist. So I think it should be True. Because every real number possible to put in the equation makes the equation true.
But whatever, I got to the main point under the minute challenge xD
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@Alexandre Sardinha – I disagree. You are changing the assumptions of the problem by saying x can never be zero. The problem states that the equality holds for all x such that x is a real number. In other words, pick any real number WHAT SO EVER and x/x will ALWAYS equal 1. Zero is a real number but 0/0 does not equal 1. Therefore, the equality does not hold for all real numbers and so the statement is false.
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@Nick Posey – If your assumption is true, then what does 0/0 equal?
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@Daniel Rothas – x/x=y can be represented in a Cartesian coordinate plane. As lim x->0-, y->Negative infinity. As lim x->0+, y->infinity. This is a discontinuous function, ergo 0/0 is possible to calculate, but trivial. QED.
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@Katrina Nichols – That's not true. As lim x->0+, you get a number slightly larger than 0 divided by the same number slightly larger than 0. That's 1, not infinity. The same thing for lim x->0-.
In fact, lim x->0 is indeterminate. Apply L'Hopital's and you find quickly that the lim as x->0 is 1. Ergo, x/x always equals 1. Context is important.
@Daniel Rothas – It doesn't have to equal anything, as long as there is the possibility that x = 0 and 0/0 is indeterminate the answer is still false
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@N Waru – It is irrevelant. No such function as 0/0.
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@Daniel Rothas – There is an operation such as 0/0, it's actually a mathematical concept. If x = 0, which it can, the expression will be 0/0 which is indeterminate.
@Daniel Rothas – 0/0 isn't a number and can't be done so it should be true
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@Donte Theiler – That fact that 0/0 is not a number is precisely the reason that the answer is false.
@Alexandre Sardinha – The question was a little bit strange because i did not understandable. Did not recognized the lay out of the question and i put false because that is what i got taught in my MATHS lessons at school that is why he told me to put false for. So is me MATHS Teacher wrong. Why????????
As others have said, 0 is a real number, but 0/0 is undefined so the answer would have to be "false"
so, if is undefined it can't define 1 (for x=0). So the answer is "false".
x cannot be 0 if you want the answer to be true. However, considering 0 is a real number, it does fall within the parameters of the question and therefore a potential candidate to be x.
X can totally be zero under the premise of the question. Zero is a real number, after all.
This is not true when x=0
Therefore the answer is False!
I think what people are not understanding is that the original question is x/x, meaning you have a non permissible value. This means no matter how you rearrange the question (looking at you x=1x people), you still have the original NPV of 0. This is because you cannot divide by zero as 1/x+ approaches positive infinity as x approaches 0 and 1/x- approaches negative infinity as x approaches 0. In other words, if you come from the positive side, you get an answer for dividing by 0 that is massively positive, and if you come from the negative side, you get an answer for dividing by 0 that is massively negative. This means there is no single value for dividing by zero, since we come up with two values that are completely different. In conclusion, you can't divide by zero, and the original question is a division statement.
- 0 0 is not equal to 1 although 0 is a real no.
if x=0 then it is 0\0 indeterminate form
If x is equal to zero then it this is not correct
It's false. The solution i thought: What if x = log y! log y / log y = log 0. And log 0 is not defined.
If x != 0, the statement is true. So therefore the answer is false
Siri tells you why 0/0 can't be done pretty well.
0/0 is indeterminate. It's like saying infinity minus infinity. You just don't know
It's not that you don't know. It's that it's meaningless. It can't be assigned a value :)
if x=0, this is false, so there you have it. There are no rules excluding 0 from this, the only rule is excluding non real values, i.e. the square root of negative one
Real numbers are any numbers on a continuous number line, regardless if it is positive, negative, rational, irrational, etc.. Because zero is part of a continuous line, and cannot be divided by zero, the answer is false.
0/0 does not equal 1, so the answer is false. However, in response to other solutions, is 0/0 really undefined? Any number divided by 0 is undefined because a/b=c is the same as a=c*b. So something like 4/0=c is unsolvable because there is no number to make 0 ∗ c = 4 . However, let's consider 0/0=0. To check if the statement is true, let's rearrange. 0 = 0 ∗ 0 . If 0 ∗ 0 = 0 is indeed true then how would 0/0 not be defined?
0 divided by 0 cannot be 1, because you cannot say that 0 goes into 0 one time. IF anything, you can say 0 divided by 0 is 0, only as a special case, because there is no value to any of the numbers...but that still does not work, because you cannot have a 0 equal groups.
Your condition that x not be equal to infinity is unnecessary. The question says for all real values of x. Infinity, in a rigorous mathematical sense, is neither real nor a number; it is an abstract idea. You can not "plug in" infinity into the equation like you could a real number.
Infinity is not a real no.
x x = 1 Only if x = 0