Is Alice's Arithmetic Wrong?

[liz]

would anyone care to explain what indeterminate and undefined mean exactly and why the obviously very significant difference is?

 

[Ivan Seeking]

I believe [but am not absolutely certain] that this an accurate representation of the difference.

0⁰ = 1

The value is indeterminate, but defined to be 1 for consistency. By this, division by zero is both indeterminate and undefined.

 

[kaos]

how does the 0 to the power of 0 will be 1. wouldn't it be 0?

i am a maths and science noob tho.

 

[hypermorphism]

how does the 0 to the power of 0 will be 1. wouldn't it be 0?

i am a maths and science noob tho.

Take a look at the function f(x)=x⁰. This motivates defining 0⁰=1 in circumstances similar to this function. Take a look at the function g(x) = 0^x. In circumstances similar to this function, we may want to define 0⁰ to be 0. This is why 0⁰ is indeterminate.

 

[Danger]

Barely anyone even knows this is a Lewis Carroll reference, let alone what the question is (Douglas Addams gives a hint in his book, not the answer).

I hadn't a clue about Lewis Carroll. I only know from the books that although 42 was the correct answer, they had asked the wrong question. Please elucidate. (even on PM if you don't want to alter reality in the thread)

And if we're voting on it, I say we make division by zero immoral.

No! Then I'd spend the rest of my life doing it! I have other plans!

 

[Gokul43201]

I hadn't a clue about Lewis Carroll. I only know from the books that although 42 was the correct answer, they had asked the wrong question. Please elucidate.

There's a part where Alice starts doing weird arithmetic saying the '4 times tables' but seemingly getting it it all wrong. She also says something like "at this rate, I'll never reach 20".

The reason the multiplication that Alice is doing is not wrong is because she is not working in base 10. Each line of her tables is in a different base (chosen from some nice sequence with differences of 3). Following the sequence, you get 4*10=17 (base 33), 4*11=18 (base 36), 4*12 = 19 (base 39) and so, you'd expect 4*13=20 (base 42). But alas ! The correct answer, base 42, will be 1A. So her tables will never see a 20 in the answer !

 

[Ivan Seeking]

There's a part where Alice starts doing weird arithmetic saying the '4 times tables' but seemingly getting it it all wrong. She also says something like "at this rate, I'll never reach 20".

The reason the multiplication that Alice is doing is not wrong is because she is not working in base 10. Each line of her tables is in a different base (chosen from some nice sequence with differences of 3). Following the sequence, you get 4*10=17 (base 33), 4*11=18 (base 36), 4*12 = 19 (base 39) and so, you'd expect 4*13=20 (base 42). But alas ! The correct answer, base 42, will be 1A. So her tables will never see a 20 in the answer !

Tsu gives her age in hex [base 16].
I just noticed that the IRS forms never specify the base to be used. Hmmm.

 

[BobG]

I hadn't a clue about Lewis Carroll. I only know from the books that although 42 was the correct answer, they had asked the wrong question. Please elucidate. (even on PM if you don't want to alter reality in the thread)

Lewis Carroll used the number 42 constantly in his books because he was addicted to Physics Forum and 42 is the answer to all of PF's important questions.

 

[jcsd]

would anyone care to explain what indeterminate and undefined mean exactly and why the obviously very significant difference is?

Undefined means that no meaning has been assigned, so in this case, as (0,0) is outside of the domain of the binary operator '/', '0/0' has no meaning assigned to it.

Something is indetermiante when it has no definte value assigned to it, for example say we take two functions and combine them into another function h(x) = f(x)/g(x). Let us say that the limits of f(x) and g(x) as x tends to some value c are both zero, then the limit of h(x) could take on any real value or not exist, so we call the limit of our general function h(x) as x tends to c 'indetereminate' (though rember it is a genarl function for a specific function the limit either exists and has a specific value or doesn't exist).

 

[Evo]

There's a part where Alice starts doing weird arithmetic saying the '4 times tables' but seemingly getting it it all wrong. She also says something like "at this rate, I'll never reach 20".

The reason the multiplication that Alice is doing is not wrong is because she is not working in base 10. Each line of her tables is in a different base (chosen from some nice sequence with differences of 3). Following the sequence, you get 4*10=17 (base 33), 4*11=18 (base 36), 4*12 = 19 (base 39) and so, you'd expect 4*13=20 (base 42). But alas ! The correct answer, base 42, will be 1A. So her tables will never see a 20 in the answer !

I never knew that! Thanks Gokul.