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Thread: How is the following bulls*it expained really? 2^0 = 1

  1. #1 How is the following bulls*it expained really? 2^0 = 1 
    Forum Ph.D. Raziell's Avatar
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    On my casio calculator we have the ^ key which multiplies the number by its own amount. Not sure what its called in english but we call it "Hatt" as in a hat you wear on your head, so 4^5 is basicly 4x4x4x4x4 or something. Basic i know, here is the problem:

    Our teatcher says 2^0 = 1

    2 times zero is friggin ZERO not one.

    There seem to be no logical explanation. I feel so dumb in math, please explain to me why TWO TIMES ZERO EQUALS ONE, it shouldnt. And because of this im scepical to all math now. If people just "Invent" rules randomly then that has to have some serious buttefly effects in math.


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  3. #2  
    Forum Professor jrmonroe's Avatar
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    If you compute 2^n as n approaches zero, you'll see that 2^n approaches 1.

    This is easier to see in a spreadsheet where the left-hand column starts with 1 and each subsequent cell under it is the previous cell divided by 2 (so the column runs: 1.000, 0.500, 0.250, 0.125, etc). The right-hand column is 2 to the power of the value to its left (so the column runs 2^1.000, 2^0.500, 2^0.250, 2^0.125, etc).

    Any base (2, 10, 1,000, etc) to the power of zero equals 1. Try it out.

    If, instead, you had the right-hand column computing 2*n, then (as you say) it would approach 0, not 1.

    The caret symbol, ^, is usually read as "to the power of", as in "2 to the power of n".

    This is not exactly a "times" function; it is a "to the power of" function. To use your example (slightly modified):

    4^5 = 1x4x4x4x4x4
    4^4 = 1x4x4x4x4
    4^3 = 1x4x4x4
    4^2 = 1x4x4
    4^1 = 1x4
    4^0 = 1

    If k^0 actually equaled 0, then any number to any power would equal 0.


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  4. #3  
    Forum Ph.D. Raziell's Avatar
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    Now that is what i call a good answer, thanks!
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  5. #4  
    Forum Bachelors Degree x(x-y)'s Avatar
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    To add to that rather good explanation, look at the 4^5 you put as am example yourself. As you said, this is the same as 4x4x4x4x4 = 1024.

    So, when you are doing 2^0, this does not mean 2x0 it means 2 to the power of zero which is essentially the same as saying 1.
    "Nature doesn't care what we call it, she just does it anyway" - R. Feynman
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