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About this app
实分析反例是一款面向数学相关专业和自学者的工具应用，把实分析里那些容易「想岔」的反例从符号推导变成可以动手试的界面。 应用按主题拆成几个模块：病态函数里可以调魏尔斯特拉斯函数的参数，看级数项增加后曲线怎么变，也能在指定点做差商探针；积分比较页面对比黎曼积分和勒贝格积分在狄利克雷函数、托马函数等情形下的差别，顺带给出达布上下和；测度反例用康托尔集等例子说明「不可数」和「测度为零」不是一回事；收敛模式页把逐点、一致、几乎处处、依测度、L几种收敛放在同一套控件下对照；分形测度模块可视化康托尔集、科赫曲线等构造，并估算豪斯多夫维数；巴拿赫-塔斯基页用分步图解解释悖论为什么依赖选择公理；工作台则把差商、达布和、体积计算等常用数值实验集中在一起。
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What you can learn from 实分析反例
Every shipping app on the App Store has gone through the same decisions you're working through right now: which screenshot goes first, what caption sits over it, which device frame to show, what color the background should be. The 3 screenshots above are 实分析反例's answers to those questions — they're public, they're real, and they made it through Apple's review.
Notice the first screenshot in particular. It's the one users see in search results and on the product page, and it's where most apps spend their best caption and tightest design. Look at the proportion of background to phone, where the text sits, what one thing the image is trying to communicate.
Want to see how other Education apps approach the same problem? Browse more Education apps in the showcase.
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