Finitists have infiltrated the US high school math textbook industry and designed a curriculum to convince students that only rational numbers exist. Here are examples of their subversion:1. Insistence on always writing answers in exact form.Certainly there is value in keeping intermediate results in exact form. But when students are trained to only ever answer questions in exact form, they fail to develop an intuition (what educators call "number sense") for irrational numbers. They will tell you the area of a circle with radius 5 cm is 25 cm^2, and think their mistake a minor one. And because they are expected to simplify [math]\sqrt{9}[/math] down to 3 but leave [math]\sqrt{2}[/math] as it is, they will say things like "there is no square root of two." I hear this come out of the mouths of otherwise highly intelligent students routinely.2. Overemphasis on factoring as a means to solve quadratic and other polynomial equations.American high school algebra classes spend an inordinate amount of time teaching how to completely factor polynomials in the ring [math]\mathbb{Z}[X][/math], to the point that when students encounter a non-contrived quadratic equation, they attempt to solve it by guessing factors and become frustrated when no factors of the form they expect exist. It makes no sense until you understand it as an effort to persuade them that irrational solutions don't exist.
>>16565497the literal opposite is true. infinity and set theory is a subversion.
>>16565497>And because they expect you to simplify sqrt(9), but leave sqrt(2)I know you’re trolling, but this “simplification” procedure is obvious to anyone who’s done ring extensions. There is an obvious ring isomorphismQ cong Q[x]/(x^2 - 9)
>>16565539I know you're trolling, but Q is a field whereas Q[x]/(x^2 - 9) has obvious zero divisors.
>>16565576It doesn't. Let (a+bx) and (c+dx) be in Q[x]/(x^2-9). Setting (a+bx)(c+dx)=0 gives the systemac + 9bd = 0bc + ad = 0which has no non-trivial solutions for (a,b).
>>16565497both of these are cool things to do and i still believe in infinity and realsanyone who has spent 5 minutes thinking about xeno's paradox must accept that real numbers exist
>>16565497omgwhat about the world's most famous number of all?namely piit's irrationaland what about the world's second most famous number of all?namely eit's also irrationaland occurs in physics and engineeringis this thread a honey pot?is /sci/ a honey pot?what kind of ridiculous board is this?good grief
>>16565622>what about the world's most famous number of all? >and what about the world's second most famous number of all? 1 and 0 are literally like, "Kek, wut?".
>>16565616a=3, c=-3, b=d=1
>>16565647kek that's rightI'm retarded
>>16565497>They will tell you the area of a circle with radius 5 cm is 25 cm^2, and think their mistake a minor one.The issue is schools assigning lots of trivial exercises, which means the students don't get to work on problems where keeping intermediate results in exact form matters. Clearly if your end goal is to know the area of a circle, "approximately 78.54 cm^2" or "between 78.53 and 78.54 cm^2" are more useful answers than "[math]25\pi[/math] cm^2". Let's have them solve problems like pic related instead.
>>16565674>solve problems like picarea(shaded region) = area(triangle)proof:https://www.wolframalpha.com/input?i=%CF%80*%28r*%E2%88%9A2%2F2%29%5E2%2F2-%28%CF%80*r%5E2%2F4-r%5E2%2F2%29
>>16565622>namely pi>namely e>>16565631>1 and 0Madonna:"I've got the moves baby, you've got the motionIf we got together we'd be causing a commotion""moves": pi and e"motion": 1 and 0"commotion": e^(i*pi) + 1 = 0
>>16566130>Ergo, QED!>[mike drop]Bravo!
