Euler Identity in Home

[Han]

(04-17-2014 08:29 PM)ColinJDenman Wrote:  I do entirely agree that returning a value is wrong. It should say divide by zero, or not a number or "I'm sorry Dave, I can't do that" or some other indicator. I favour the approach that the calculator tells you that your going near its limitations rather than giving a value that can potentially roll through into further calculation. I liked this example because it is a) obviously wrong and b) too big to justify as a small thing like the 2E-13 stuff.

If you wish, "a calculator's gotta know its limitations". Or I need a shotgun:
http://www.hpmuseum.org/forum/thread-1103.html

Your references are indeed interesting. Thanks.

From the third link is this example for the TI-83.
\[ 5^{14} = 6103515625 \]
\[ Ans/4 = 1525878906 \]
So apparently 5^14 is divisible by 4. Then we check what the calculator is really thinking:
\[ Ans - 1525878906 = .25 \]
Quoting the article:

Quote:Of course, the calculator doesn’t really believe that 5^14 is even as is seen when we subtract the apparent answer from itself. I will leave it to the calculator manufacturers to explain in detail what causes this “lie”. I’ll just say it seems to have something to do with the fact that the actual value of 5^14 ÷ 4 has one more digit than it’s able to display precisely and it won’t resort to scientific notation because 5^14 could be expressed precisely.