syops

10 ms·

31.
by syops 5y ago
I don’t give a definition. The students know real numbers are the “decimal numbers”. They don’t need to know a definition at this point and giving one more precise than “decimal numbers” will just confuse them. They gain familiarity by p
32.
by syops 5y ago
There is no such example. All real numbers are either rational or irrational.
33.
by syops 5y ago
The algebraic closure of the rationals is not the reals. The reals are the completion of the rationals using the standard metric. The intention of my post was to point out the complexity of not brain washing students at a low level. Your
34.
by syops 5y ago
It depends on your mathematical background. I don’t know of any books about this at the level below senior undergraduate mathematics. If you are familiar with sets I can outline the idea behind how to define non negative integers. We assu
35.
by syops 5y ago
Here’s the definition of 2 using the standard construction with the Peano axioms. It’s the set containing 0 and 1. The number 1 is the set containing 0 and 0 exists by one of the axioms. It’s not something a person in intermediate algebr
36.
by syops 5y ago
I think it’s clear you’ve never taught low level mathematics courses. There is a lot of hand waving and brain washing that happens. The vast majority of people don’t know what a number is in a precise, mathematical sense. At the level of
37.
by syops 5y ago
That’s a better term to use. Thanks for the suggestion.
38.
by syops 5y ago
I used the phrase in a colloquial sense. Replace mentally disabled with intellectually disabled. That’s the proper modern term for what was once called mental retardation. I gave no indications that people ought to be ranked in terms of v
39.
by syops 5y ago
Oh, I’ve thought a great about these things. None of your questions are new to me or are ones I’ve not considered. I did not come to my conclusion quickly. Here are some more thoughts to ponder: Children are easier to brain wash than adul
40.
by syops 5y ago
It’s interesting reading the responses of people who never taught in the classroom.
41.
by syops 5y ago
It’s easier to type retarded than intellectually disabled on an iPad. I wrote the modern version in my original comments. Clearly I have been discussing this topic in a detached way. You’ve formed an image in your mind about me that isn’t
42.
by syops 5y ago
I don’t claim that there is a partial order to intelligence. Indeed, I think it’s clear that no such can exist. Let me put it this way. The set of people who can’t learn algebra (using any reasonable standard for this) is nonempty as it
43.
by syops 5y ago
There’s no onus on either of us to do anything. We are just strangers posting on the internet without pay or other compensation. Your experience and knowledge about teaching help me to decide the merits of your beliefs. It appears from m
44.
by syops 5y ago
Yes, this has long term negative effects but I need a job and don’t need the stress of being hounded by administration. In the old days the state funded a much higher percent of a student’s higher education. In those days, society was the
45.
by syops 5y ago
I can accept your belief, in principle, about putting enough effort in early education and that lack of such efforts contributes to poor outcomes in college. I also think though that some people just can’t grok algebra. You would agree th
46.
by syops 5y ago
It’s not a sufficiently difficult topic for you. Have you ever taught algebra to a classroom of people from a wide range of intellectual capabilities and experiences? Are you even aware of some of the pain points to learning algebra?
47.
by syops 5y ago
My belief comes my experience teaching math the past 20 years. I think we both agree that mentally disabled people can’t learn algebra. Do you have any evidence that these are the only people incapable of learning algebra? I have lots of
48.
by syops 5y ago
From the article: Over the next year, a biosciences working group revised the program’s funding guidelines, stipulating in the final draft that it would not support any research into the first-order effects of genes on behavior or social o
49.
by syops 5y ago
The problem with never consenting to a search or never talking to police is the ease with which cops can ruin your weekend (and even life) if they get pissed off at you. I may be able afford a lawyer but is the night in jail worth the effo
50.
by syops 5y ago
Sometimes government, sometimes the individual. It’s a balancing act. My neighbor might think it’s in his best interest to dump toxic waste on his property because he needs/wants money. In this case, thankfully, government is there
51.
by syops 5y ago
Yes, in economics this is called an inferior good. This does not make public transportation a bad investment or mean that society wouldn’t be better off overall with it. We are local optimization machines and sometimes our desires are not
52.
by syops 5y ago
I now understand and agree with your point.
53.
by syops 5y ago
Nothing would be decimated if we yanked those funds other than our ability to destroy other nations. We could build a much better social safety system that covers far more people. It’s not as if military spending is the only option as far
54.
by syops 5y ago
We could have done both. Opponents of rail decry it’s apparent inefficiency and call it wasteful spending. Even assuming it is wasteful spending it’d still have been much better spending $6 trillion on building trains than on the wars. H
55.
by syops 5y ago
It depends on how one measures poorer. Economists will look at a society with more cars per person as a good sign. I view it as a bad one if the country is already wealthy. The profligacy of Americans is obscene and makes us poorer in sp
56.
by syops 5y ago
According to this Adam Tooze article the wars cost around 800,000 dead people. Then there is the incalculable emotional cost to survivors and participants. This alone means that spending $6 trillion building trains would have been much be
57.
by syops 5y ago
Yeah, the demographic density argument fails to hold up to the fact that spending $6 trillion on high speed rail would have been much more beneficial to society than spending it on Iraq/Afghanistan.
58.
by syops 5y ago
In 1995 China and the U.S. both had essentially zero miles of high speed rail. Today China has tens of thousands of miles of high speed rail and the U.S. still has essentially zero miles of high speed rail. We did invest $6 trillion in 20
59.
by syops 5y ago
I don’t understand your overall point. Bringing up anti-vax people the way you did suggests to me that perhaps you have become lost. Being an anti-vax person is objectively foolish and dangerous. We have decades of incontrovertible evide
60.
by syops 5y ago
Yes to both questions. Neither question is really relevant though. In the hierarchy of needs it’s easier to fill the lower level ones in the U.S. than in El Salvador. People move to the U.S. for ease of meeting needs, to experience the U

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