I discovered that many calculators (like the one built into Google) can make some crazy mistakes, so I began investigating different ways to break a calculator...
0:00 - Introduction
0:43 - Comparing a couple calculators
2:20 - Error messages vs. mistakes
3:02 - Mistakes with infinity and zero
4:46 - Problems with almost integers
6:36 - Mistakes with the number pi
7:41 - A graphing calculator mistake
8:23 - Multiple mistakes with the number e
11:10 - Mistakes with larger size differences
12:33 - Answers with the completely wrong sign
13:01 - Overall conclusions
14:01 - Credits
Some notes in response to some comments I saw on this video:
Lots of people are commenting about reasons why Google's calculator has things stored internally in these ways, like how it uses "infinity" to refer to overflow errors in its internal code. While that's true, it's still the calculator's job to translate its internal code into an output that humans can understand, so it's silly that they keep that output as saying "infinity" as opposed to translating it into some type of error message.
Overall, the Google calculator isn't forced to use this exact type of code translated in this exact way, and if you compare it to the accuracy of some other calculators, you can see lots of room for improvement...
Maybe in the future I'll make a video analyzing the limitations of "floating point arithmetic" that explains the mathematics of some of these errors, but this video was more about showing the current problems that can emerge from ways it is implemented and translated through specific calculators.
Also, some people are saying that all of the errors are just "rounding errors", but I feel like we need a different term for times when rounding errors compound in such an intense way that they cause the given answer to be vastly different than the correct answer, because that's not what "rounding error" usually implies.
Also, with the last few calculator mistakes, one commenter wondered about how it looks like the exponents are inside the parentheses on one calculator and outside the parentheses on the other calculator. I copy/pasted the exact text into each calculator, and they just have different ways of formatting the parentheses when showing the expression you searched, but it is functionally the same on both. Regardless of how you format this aspect of it, that is not the reason for those errors.
Thanks for watching!
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This episode of Combo Class was created, directed and edited by me (Domotro) and I also made all of the music in it. It was filmed by me and Carlo Trappenberg.
Mathematical topics in this video include: various calculators including the most commonly used online calculator on Google, the better free calculator on Wolfram Alpha, the graphing calculator Desmos, calculator mistakes, error messages, divide-by-zero errors, infinity, zero, almost integers, the number pi, the number e, and various other fun things.
Disclaimer: Do not copy any potentially dangerous actions you may see in these videos, such as any actions related to fire, glass, or tools.