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Exponentiation to zero annoyed me as a kid because I had equated "no operations" as zero from the pattern 2x2=2+2, 2x1=2, 2x0= Declaring 2x2=0+2+2, 2x1=0+2, 2x
by jon_richards 2y ago
Exponentiation to zero annoyed me as a kid because I had equated "no operations" as zero from the pattern 2x2=2+2, 2x1=2, 2x0=
Declaring 2x2=0+2+2, 2x1=0+2, 2x0=0 while 2xx2=1x2x2, 2xx1=1x2, 2xx0=1 seemed arbitrary.
What helped was learning about negative exponentiation and exponentiation simplification, so 2xx0 = 2xx2 x 2xx(-2) = 2xx2 / 2xx2 = 1.
That said, I clearly still take issue with unintuitive interpretations of "nothing" https://stackoverflow.com/questions/852414/how-to-dynamically-compose-an-or-query-filter-in-django/59762852#59762852 https://stackoverflow.com/questions/852414/how-to-dynamicall...
- whatshisface 2y agoAnother good way of thinking about it is that if 10^a 10^b = 10^(a+b), you can set a=3 and b=0 to get 10^3 10^0 = 10^3. If you divide both sides by 10^3, 10^0 = 1. QED.
- anon291 2y agoI mean the reality is that in the same way that 2 * 0 is ONE. Or if I were using latex: 2 \times 0 = 1_{+} Because multiplication, being repeated addition and exponentiation repeated multiplication both behave the same way. When asked to repeat the operation zero times, they return the unit or 1 of the underlying group, which is typically denoted as 1_{whatever} However, the 1 of addition is 0 when using the standard notation for integers
- bmacho 2y ago> Exponentiation to zero annoyed me as a kid Your teacher didn't tell you (or told you, but you didn't recognize it as something valuable and forgot it) that exponentiation to zero is a new definition over exponentiation to positive integers. Exponentiation to positive integers is defined somehow, and that definition says nothing about exponentiation to zero. It is a new definition, not something that you deduce. The same holds for 0^0 or 0/0 (with some amounts of confusion, lies, and hypocriticism).
- jon_richards 2y agoDeclaring it as a new definition was what annoyed me... Which I found incredibly silly once I leaned about negative exponentiation and could now deduce the pattern. Similarly, 0/0 became much more tractable to me once I learned L'Hôpital's rule https://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule https://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule
- deleted 2y ago[deleted]
- n_plus_1_acc 2y agoNow, you probably now that this is because 0 and 1 are the identity elements of the additive and multiplicative groups of real numbers, respectively. Probably wouldn't've helped you as kid though
- jon_richards 2y agoI think it's much more productive to teach children 2x0 = 2x1 + 2x(-1) = 2-2 = 0 and 2xx0 = 2xx1 x 2xx(-1) = 2/2 = 1 Inverting the concept and having those patterns stem from a fundamental identity can wait until its not seen as the mathematical equivalent of "Because I said so".
- Etherlord87 2y ago"Children" at what age do you want to teach this, and how many children are you in contact with? Because that one kid probably suffers from autism.