
What is 1 divided by 0?
Answer
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Hint: We need to find the value of 1 divided by 0. We start to perform a division considering number 1 as a dividend and the number 0 as a divisor. Then, we write all the cases encountered during the division to get the desired result.
Complete step by step solution:
The division of a real number with the real number is given as follows,
Here,
is the dividend of the division
is the divisor of the division
Assuming the real number is the result of the above division.
Writing the expression for the same, we get,
Cross-multiplying the number to the other side of the equation,
Now,
According to our question,
Assume that the value of is equal to 0.
If is the non-zero real number, there is no value of such that, if multiplied by the number , gives a non-zero real number since the product of any number with the number 0 is always 0.
Even if we consider the value of , the real number can take any number that is multiplied by to give the result as the number 0.
From the above cases,
We can say that the division by the number 0 is undefined among the set of real numbers.
The result of 1 divided by 0 is undefined.
Note: We must remember that the value of 1 divided by 0 is infinity only in the case of limits. The word infinity signifies the length of the number. In the case of limits, we only assume that the value of limit x tends to something and not equal to something. So, we consider it infinity. In normal cases, the value of 1 divided by 0 is undefined.
Complete step by step solution:
The division of a real number
Here,
Assuming the real number
Writing the expression for the same, we get,
Cross-multiplying the number
Now,
According to our question,
Assume that the value of
If
Even if we consider the value of
From the above cases,
We can say that the division by the number 0 is undefined among the set of real numbers.
Note: We must remember that the value of 1 divided by 0 is infinity only in the case of limits. The word infinity signifies the length of the number. In the case of limits, we only assume that the value of limit x tends to something and not equal to something. So, we consider it infinity. In normal cases, the value of 1 divided by 0 is undefined.
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