Equality check for double type gives strange results in C++

Question

I have the following code:

#include <iostream>
#include <math.h>
#include <vector>

int main() {
    size_t N = 20;
    double from = 0.0;
    double to = 1.0;

    std::vector<double> xVec{};

    double h = (to - from) / double(N);
    for (double x = from; x <= to; x += h) { // not entering x == 1.0
        xVec.push_back(x);
        std::cout << x << "\n";
    }

    std::cout << "\n";

    double x = 0.9;
    const std::vector<double>::iterator it = std::lower_bound(xVec.begin(), xVec.end(), x);
    std::cout << x << " " << *it << " " << (x == *it) << "\n"; // states that 0.9 != 0.9
}

Which gives this really strange output:

0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95

0.9 0.9 0

I have 2 questions about this:

1. Why is my loop not entering x == 1.0, when I am using <= in the loop criterion?
2. How is it possible that a double given by std::lower_bound is not equal to another double with the same value?