True or False?
By the law of indices, we know that a 3 = a × a × a and a 2 = a × a .
This also means that a 2 a 3 = a × a a × a × a = a × a a × a × a = a .
Let a = 0 , we get 0 2 0 3 = 0 .
Since 0 3 = 0 × 0 × 0 = 0 and 0 2 = 0 × 0 = 0 , we can conclude that 0 0 = 1 .
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What does [1] mean?
0÷0 is undefined, as Siri for Apple says when asked. Siri replies: “Imagine that you have zero cookies and you split them evenly among zero friends. How many cookies does each person get? See? It doesn’t make sense. And Cookie Monster is sad that there are no cookies, and you are sad that you have no friends.”
Stop it! This is too real for me.
Well division by 0: it's just a no go in any case ;)
Yeah, would you like to explain why "division by 0" is prohibited? The education system always implement this rule, but I doubt I ever heard a teacher that properly explain why this is prohibited...
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I usually use a cheesy example to illustrate it(not really mathematical though, but for teenagers it's clear): imagine its my birthday. I always wanted to believe I am very popular, so I invite lots of people to my party. And of course I will be lots of pies to celebrate with them. But... When the moment is there I turn out to be a loner and nobody shows up. Now is it possible to divide those pies over 0 'friends'? (and I can't take the pies myself because of my diet)
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I will buy*
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Now is it possible to divide those pies over 0 'friends'?
Well, you just don't split the cake, isn't it?
The proper way to answer this is to think about "When can an inverse function exist?"
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@Pi Han Goh – Yeah of course, but... Teenagers of the age 12~18 who have math because they have to and not because they choose to will be like: 'huh, inverse function?' ;p
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@Peter van der Linden – really? teenagers below age 18 never heard of inverse function? I seriously doubt that's true... oh well....
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@Pi Han Goh – Well it's complicated. It has to do with the educational system over here in the Netherlands.
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@Peter van der Linden – That sounds depressing.... ;(
0 ÷ 0 = x → 0 = x × 0 ⇒ All number of x enters to the equation in the range of complex number, the equation is always true, but we cannot define the answer, so it is Undefined!!!
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In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0 where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 also has no defined value; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst ("ghosts of departed quantities").
There are mathematical structures in which a/0 is defined for some a such as in the Riemann sphere and the projectively extended real line; however, such structures cannot satisfy every ordinary rule of arithmetic (the field axioms).
In computing, a program error may result from an attempt to divide by zero. Depending on the programming environment and the type of number (e.g. floating point, integer) being divided by zero, it may generate positive or negative infinity by the IEEE 754 floating point standard, generate an exception, generate an error message, cause the program to terminate, result in a special not-a-number value, a freeze via infinite loop, or a crash...................................wikipedia