Plz tell what exactly is wrong here and WHY?
- Thread starter TMarvel
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Harry_the_cat
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Because division by 0 in the third step is not defined.
What is wrong here is a matter of definition.
The definition of exponents that you were probably taught in elementary school is historically accurate, but does not reflect the current meaning of exponents in mathematics. You were probably told something like “an exponent indicates how many times a number is multiplied by itself.” That definition makes no sense with respect to exponents that are not integers greater than 1.
A more modern definition that is used by some is
[math]r^0 = 1;\ n \text { is a positive integer } \implies r^n = r * r^{(n-1)}.[/math]
Following that definition, [imath]0^0 = 1[/imath] BY DEFINITION.
When, however, we want to talk about exponents that are not integers, that definition cannot apply. A simple definition wiil not work unless the r in [imath]r^x[/imath] is greater than zero. So under that definition, [imath]0^0[/imath] is undefined.
See https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero
The definition of exponents that you were probably taught in elementary school is historically accurate, but does not reflect the current meaning of exponents in mathematics. You were probably told something like “an exponent indicates how many times a number is multiplied by itself.” That definition makes no sense with respect to exponents that are not integers greater than 1.
A more modern definition that is used by some is
[math]r^0 = 1;\ n \text { is a positive integer } \implies r^n = r * r^{(n-1)}.[/math]
Following that definition, [imath]0^0 = 1[/imath] BY DEFINITION.
When, however, we want to talk about exponents that are not integers, that definition cannot apply. A simple definition wiil not work unless the r in [imath]r^x[/imath] is greater than zero. So under that definition, [imath]0^0[/imath] is undefined.
See https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero