You joke, but there are people that are overboard on this. It's fun to them to calculate how much stress a joint is under to determine the most efficient, in terms of materials used, joint. Most of them seem to be older and were raised by people who lived through the Great Depression or lived through it. My Grandfather and father were those types. My dad had a shed he built dressed down by his father. Apparently the exchange was "excessive and lazy application of metal fasteners" and somewhere in there my GF also said "math is what separates us from the animals. If you don't use it, you're no better than they are".
i'm not sure how i fit, because in a lot of ways i'm a math person. i'm not good at writing songs, even though i've tried a little bit. I just don't see the world in a way that puts it into that format...so, i guess i see the world more math-ly. I liked it in school, because i could usually tell when i got to the end if i had the right answer or not. But i have little to no interest in understanding or caring to understand more complicated stuff. i didn't have to do much math in college and that was fine by me. i do have a good brain for language, it's not terribly difficult to learn a new one, for me. but i'm like you on reading, i love to read, but i don't get off on dissecting all that crap we talked about in english class in high school. i always doubted whether nathaniel hawthorne or shakespeare really meant for us to dig in and find all that garbage.
Math and language use the same areas of the brain. Music as well. Though creating music might be a little different.
LOL...My FIL built an addition onto our house. I helped and did most of the grunt work. We added a 300 sq ft new master bedroom with full bath for ~$6K. We dug the trough for the footers by hand. We recycled block from the wall we took out. There were no contractors. He measured constantly and everything was very detailed. Everything was to code or better. He got the big code book that they use at the county office. The inspector came out and gave him a hassle because he had never before seen some of the things the FIL had done. The final conflict was when the inspector saw that there was no engineering stamp on the trusses. My FIL is a PhD. in Chemical Engineering and a retired Major from the Airforce. Inspector: "Are you an engineer?" FIL: with disgust and impatience in his voice "Yes I am!" I had to hide my laugh. That was the end of that. But the uncle in law/ FIl little brother came over to help one day. He believes rough carpentry means rough carpentry. He is a PhD. in Physics and is retired from ORNL. To say there was tension would be to put it mild. Fortunately for me I was only there half the day as I had to take care of a client and had to leave! My wifes grandfather passed last spring and he was 98. He was still going strong until about 2 years ago. He built his own house and the boys helped him do it. He was a WW2 vet and raised during the Great Depression. He worked on it on weekends and paid as he went. I think they said it took 5 years.
When I'm driving, I do physics problems in my head to estimate arrival times, etc. I used different approaches to see which one worked best (average vs time weighted averages and such). I do the same thing when I run. Otherwise, I use it for work, but math for the sake of it is not my thing. I'd speculate it's those people Norris waxed about in the original post that were responsible for the junky, cart before the horse math my kids and I struggled with in elementary school.
when i'm driving, I look at the gps to see arrival time and mathematize that the faster I drive, the more time it cuts off. Ya'll are no geniui
1/3 is exactly equal to .3 repeating. 1/9 is exactly equal to .1 repeating. 99.9 repeating is exactly equal to 99.9 repeating. Now you have apples to apples. The limit of 99.9 repeating is 100. It’s so close to being 100, that we can say it’s 100. So we say it’s 100. But identity says it’s exactly equal to 99.9 repeating. So I don’t get your fractions example.
If 1/9 is exactly equal to .1 (repeating), what is 9/9 exactly equal to? .9~ is a rational number, meaning it can be written as p/q where p and q are irreducible integers. What are p and q for .9~? Between any two Real numbers there is another Real number. Give me a Real number between .9~ and 1. We can argue limits, we can dismiss proofs, but the above questions demand answers, and the only answers are that .9~ and 1 are the same point on the Real number line, aka they are equal. It is a quirk of the decimal notation system that any terminating rational number has two decimal notations for it. There is nothing mystical or weird about it, just a quirk. And if .9~ and 1 are not equal, it breaks algebra and the Real number system.
Let's take an easy one. What's the real number between 0.19 and 0.2? Well, we'd say its 0.199. So the number between 0.19 and 0.2 is a number that is grown via decimal point. The number between them is a number with a new exposed decimal point. And there are infinite ones I can put. But its clear that 0.19 and 0.2 aren't the same. The real number between 0.9.. and 1 is 0.99.. I grow the precision to the right, the same way as between 0.19 and 0.2. And you can say that 0.9.. occupies all decimal places simultaneously, and that is wrong. The numbers between 0.19 and 0.2 occupy all decimal places simultaneously as well, but we have to expose that next decimal point to show the difference. And we can do that with a number that repeats itself: 0.9.. < 0.99.. < 0.999.. < 0.9999.. < 0.9..9.. But since the difference between all those numbers only gains us precision in our next calculation, and 0.999999999 < 0.9.. we take the next closest number, which is 1, and say "good enough." But they are not equal.
To me it seems you keep mentioning precision as if this was an engineering problem where you are measuring the length of a steel beam and you can only get to 3 decimal places with precision, and that you need a better instrument to get to a better significant digit. It is not engineering. It is infinitely precise. There are 9s in every decimal place after the decimal. All of them. There is no point "out there" somewhere where there may or may not be a 9. All of the places after the decimal have a 9. There are infinite number of them. That is the number I am defining and giving you. It doesn't change. So, I give you .9~ and 1. Give me a Real number between them.
That big shiny screen in the middle of your dashboard will do that for you. I'm also told that if you ask the google, he will tell you.
