一道离散证明可数题show that the set of all real numbers that are solutions of quadratic equations a^2x+bx+c=0,where a,b and c are integers,is countable.意思是证明当a,b,c都是整数时,a^2x+bx+c=0的所有的解释可数的,
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![一道离散证明可数题show that the set of all real numbers that are solutions of quadratic equations a^2x+bx+c=0,where a,b and c are integers,is countable.意思是证明当a,b,c都是整数时,a^2x+bx+c=0的所有的解释可数的,](/uploads/image/z/15062139-27-9.jpg?t=%E4%B8%80%E9%81%93%E7%A6%BB%E6%95%A3%E8%AF%81%E6%98%8E%E5%8F%AF%E6%95%B0%E9%A2%98show+that+the+set+of+all+real+numbers+that+are+solutions+of+quadratic+equations+a%5E2x%2Bbx%2Bc%3D0%2Cwhere+a%2Cb+and+c+are+integers%2Cis+countable.%E6%84%8F%E6%80%9D%E6%98%AF%E8%AF%81%E6%98%8E%E5%BD%93a%2Cb%2Cc%E9%83%BD%E6%98%AF%E6%95%B4%E6%95%B0%E6%97%B6%2Ca%5E2x%2Bbx%2Bc%3D0%E7%9A%84%E6%89%80%E6%9C%89%E7%9A%84%E8%A7%A3%E9%87%8A%E5%8F%AF%E6%95%B0%E7%9A%84%2C)
一道离散证明可数题show that the set of all real numbers that are solutions of quadratic equations a^2x+bx+c=0,where a,b and c are integers,is countable.意思是证明当a,b,c都是整数时,a^2x+bx+c=0的所有的解释可数的,
一道离散证明可数题
show that the set of all real numbers that are solutions of quadratic equations a^2x+bx+c=0,where a,b and c are integers,is countable.
意思是证明当a,b,c都是整数时,a^2x+bx+c=0的所有的解释可数的,
一道离散证明可数题show that the set of all real numbers that are solutions of quadratic equations a^2x+bx+c=0,where a,b and c are integers,is countable.意思是证明当a,b,c都是整数时,a^2x+bx+c=0的所有的解释可数的,
a,b,c固定时解有限(1或2,重根算1个)
a,b,c是可数的有限次方,可数,
按这个顺序排列可数个方程,其中的解未出现过的数依序列出即可(其实推广到有理数系数有限次多项式出来的代数数都是可数的)
因为三元组(a,b,c)是可数的(N*N*N=N,对角线法),而每个三元组(a,b,c)对应的方程ax^2+bx+c=0最多有两个实数根,那么所有这样的方程的根也是可数的
countable是有限数的意思啦,这道题其实就是讨论方程a^2x+bx+c=0的解的情况,很多网和参考书上都有哎