What Does the World ACTUALLY Look Like? #shorts
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To prove that a contraction mapping (f) is continuous, consider the definition of a contraction: (d(f(x), f(y)) leq c cdot d(x, y)) for all (x, y in X), where (c < 1). This implies that for any (epsilon > 0), you can choose (delta = frac{epsilon}{c}) to ensure continuity.
To show (f) has at most one fixed point, suppose (f(z_1) = z_1) and (f(z_2) = z_2) for (z_1, z_2 in X). Then, (d(z_1, z_2) = d(f(z_1), f(z_2)) leq c cdot d(z_1, z_2)). Since (c < 1), this implies (d(z_1, z_2) = 0), and hence, (z_1 = z_2), demonstrating uniqueness.
For an example of a nonempty (X) with a contraction map without a fixed point, consider (X = [0, 1]) and (f: X rightarrow X) defined by (f(x) = frac{x}{2}). This is a contraction, but it has no fixed point.
To show that if (X) is nonempty and complete, every contraction map has a unique fixed point, you can use the Contraction Mapping Theorem, which asserts that in a complete metric space, a contraction map always has a unique fixed point.
The Mercator projection stretches land to make the ocean more accurate, as that was important for ships. This projection stretches the ocean to make land more accurate.
That isn’t the Mercator projection
Weellll there is land underwater☠️🧐
E
Antarctic real: 👍
Antarctica mercator: 💀
The map in bottom right corner is not the Mercator projection…its the Plate Carrée projection
when I was young and looked at a world map I thought Antarctica was the biggest continent because it took up all the bottom
That's not the mercator. The mercator doesn't have those border sizes.
Why is Iceland so far away
Maps 🗿
The true asia is weird
This caused me to stop watching the original video
"erm, actually, that is the equirectangular projection"
Every Continent/island/ocean/sea: normal
Indian Ocean: I own half of the world
That’s interesting Jack
Hi jack
This is trippy but also surprising
Top 15 comments!
This version stretches the ocean, just not the land. The oceans are still huge, but not as huge as they appear in this map.