I could tell in edge that right side was muted based on the icon next to the address bar and noticed you could use arrows to move one by one so just pressed left 25 times.
School calculus is hated because it's typically taught with epsilon delta proofs which is a formalism that happened later in the history of calculus. It's not that intuitive for beginners, especially students who haven't learn any logic to grok existential/universal quantifiers. Historically, mathematics is usually developed by people with little care for complete rigor, then they erase their tracks to make it look pristine. It's no wonder students are like "who the hell came up with all this". Mathematics definitely has an education problem.
IMO, the calculus is taught incorrectly. It should start with functions and completely avoid sequences initially. Once you understand how calculus exploits continuity (and sometimes smoothness), it becomes almost intuitive. That's also how it was historically developed, until Weierstrass invented his monster function and forced a bit more rigor.
But instead calculus is taught from fundamentals, building up from sequences. And a lot of complexity and hate comes from all those "technical" theorems that you need to make that jump from sequences to functions. E.g. things like "you can pick a converging subsequence from any bounded sequence".
In Maths classes, we started with functions. Functions as list of pairs, functions defined by algebraic expressions, functions plotted on graph papers and after that limits. Sequences were peripherally treated, just so that limits made sense.
Simultaneously, in Physics classes we were being taught using infinitesimals, with the a call back that "you will see this done more formally in your maths classes, but for intuition, infinitesimals will do for now".
Or you can hand wave a bit and trust intuition. Just like the titans who invented it all did!
The obsession with rigor that later developed -- while necessary -- is really an "advanced topic" that shouldn't displace learning the intuition and big picture concepts. I think math up through high school should concentrate on the latter, while still being honest about the hand-waving when it happens.
I broadly agree. But, the big risk here is that it's really easy for an adventurous student to stretch that handwaving beyond where it's actually valid. You at least have to warn them that the "intuitions" you give them are not general methods, just explanations for why the algorithms you teach them do something worthwhile (and for the ones inclined to explore, give them some fun edge cases to think about).
You can do it with synthetic differential geometry, but that introduces some fiddliness in the underlying logic in order to cope with the fact that eps^2 really "equals" zero for small enough eps, and yet eps is not equal to zero.
calculus works... because it was almost designed for Mechanics. If the machine it's getting input, you have output. When it finished getting input, all the output you get yields some value, yes, but limits are best understood not for the result, but for the process (what the functions do).
You are not sending 0 coins to a machine, do you? You sent X to 0 coins to a machine. The machine will work from 2 to 0, but 0 itself is not included because is not a part of a changing process, it's the end.
Limits are for ranges of quantities over something.
The increase in temperature is just one of the issues. It has probably been mainly publicized as it's an easy "key performance indicator" to get the point across/that can be succinctly referred to. Sea level rise, ocean acidification, global weather pattern shifts, etc. are all also major problems.
There's a conflict of interest on the part of car manufacturers, if insurance just pays out and they get to do another sale, they're happy that your car got stolen.
Also, I agree with the main point of the article, but it shouldn't be so easy for any 16yo Tom, Dick or Harry to buy a gadget and start stealing cars. If it's so easy to make with off the shelf parts, then let the 'security experts' create their own.
Consumers need to be educated about keeping their keys away from doors/in a faraday cage.
If insurance pays out often enough that this might actually work as a sales tactic, they don't get another sale, everyone goes to another manufacturer because insurance is so expensive.
Also most car dealers make more profit from ongoing maintenance and servicing than selling you a new car.
Where can I get more information on this? Wasn't fukushima total disaster in that it was badly maintained and in a bad location? These two pre-conditions don't seem to apply to the plants germany had.
Exactly, we're already breathing all kinds of dangerous substances from multiple sources, why add another one.
Honestly, since they banned indoor smoking and having people smoke 9m from doors, I don't mind it. What I do mind is people throwing butts all over the place, for some reason, even people who avoid littering don't think twice about throwing their dirty butts everywhere. Every time spring comes and snow starts melting it's so disgusting everywhere.
I started smoking pipes at 15. I would grow and age my own tobacco. I love cigars, but don't like the lack of dosage control. Pipes are my absolute favorite form of tobacco use. Nothing like a little latakia in a nosewarmer while choring in the snow.
Cigarettes are tasty, but if I have a couple in a row it hurts my lungs, so I smoke very few of them.
Cigars are a lot of commitment and make me feel sick, though. Hitting a little under one dart a month after my designated club night is a real sweet spot
"normally" the court has to apply strict interpretation of the written text. if that strict interpretation leads to ambiguity or confusion or logical fallacy, then the court has to see the "legislative intent" of why the enactment was made in the first place in order to come to a reasonable conclusion as to what the framers of the law intended to be.
if the word written is "and" meaning +, that would imply in strict sense that this is a condition that has to be followed along with other conditions.
now, if someone says no, the legislative intent was not to be + but "or" because the enactment wants to provide relief and not to incur more punishment, and that applying the "+" interpretation would violate my fundamental rights, then the court can decide if the loose definition is justified from the legislative intent and can accept the same.
I don't think anybody really agrees with that position. Let's take an extreme example
The second amendment is: A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
The definition of an armament according to Britannica is: military weapons that are used to fight a war
Nuclear bombs have been used by the US military to fight a war. By your logic the right of the people to have nuclear bombs is protected by the second amendment.
In what fantasy world does "well regulated" and "anyone can own nuclear weapons" co-exist?
The whole argument about the 2nd Amendment is because it's so vague and ambiguous. If it had just clearly said "Each citizen is permitted to own a flintlock musket, 2 flintlock pistols, and a cavalry sword" (which was probably much closer to the intent of the Amendment) then we wouldn't have such a big issue with gun control. Then again, we might just have fully automatic assault "muskets".
In any case, even if you were allowed to own a nuclear weapon, that doesn't mean that you can afford one. You're allowed to own a Blackhawk helicopter or a HEMMT too, but do you? Herein lies the problem of gun ownership as a "right". Does that mean that people should be provided with guns for free?
>In what fantasy world does "well regulated" and "anyone can own nuclear weapons" co-exist?
Define well regulated and explain how it had anything to do with excluding certain types of weapons.
>The whole argument about the 2nd Amendment is because it's so vague and ambiguous. If it had just clearly said "Each citizen is permitted to own a flintlock musket, 2 flintlock pistols, and a cavalry sword" (which was probably much closer to the intent of the Amendment) then we wouldn't have such a big issue with gun control. Then again, we might just have fully automatic assault "muskets".
This is utterly ridiculous. There were rudimentary automatic weapons (puckle guns) that existed decades prior the Constitution.
Second, private citizens owned the same weaponry as the military. Canons, guns, ships, etc. If the founders wanted to limit the citizens they would have said that was their intention.
Third, if you want to take the interpretation that says only things that existed at the time qualify, then surely you are consistent and don't think the first amendment applies to the internet? Or do you just hold that standard for the 2nd amendment.
>In any case, even if you were allowed to own a nuclear weapon, that doesn't mean that you can afford one.
True, but irrelevant.
>You're allowed to own a Blackhawk helicopter or a HEMMT too, but do you?
I don't have any intention of owning either or nukes for that matter.
>Herein lies the problem of gun ownership as a "right". Does that mean that people should be provided with guns for free?
I don't think rights means you should necessarily be provided it. I don't think the government owes me free electricity and computer so I can exercise my first amendment rights for example. And before you say that example is dumb, remember that people are pushing the idea that the internet is a right. Well the internet is useless without a computer/phone. And a computer/phone is useless without electricity.
Regardless of your wish that guns are not a right, they are considered one in the US. If the US pushes the idea that healthcare is a right and as such it must be free, then I would support a lawsuit that demanded free guns from the government. I believe in consistently applying standards.
Also if it were intended as "meeting all of the criteria disqualifies you", then part A is completely redundant, isn't it? If B and C are true then A is also true.
