Injective metric space
Imagine you have a big box with a lot of toys in it. Each toy is different and has its own unique name. Now imagine you have a smaller box that can only fit some of the toys in the big box. You can pick any toys you want to put in the smaller box, but you can't put the same toy in the smaller box twice.
In math, we call the big box a metric space, and we call the toys points. Each point has its own unique name, just like the toys in the big box. The smaller box is a subset of the big box, and we call it an injective subset if we can pick any two different points in the smaller box, and they will have different names.
For example, imagine we have a metric space that represents all the countries in the world, and each country is a point in the space. Now imagine we have a subset of that space that represents all the countries in North America. This subset is an injective subset because if we pick any two different countries in North America, they will have different names.
Overall, an injective metric space is just a fancy math term that means we can pick any two different points in a smaller subset of a bigger space, and they will always have different names.
In math, we call the big box a metric space, and we call the toys points. Each point has its own unique name, just like the toys in the big box. The smaller box is a subset of the big box, and we call it an injective subset if we can pick any two different points in the smaller box, and they will have different names.
For example, imagine we have a metric space that represents all the countries in the world, and each country is a point in the space. Now imagine we have a subset of that space that represents all the countries in North America. This subset is an injective subset because if we pick any two different countries in North America, they will have different names.
Overall, an injective metric space is just a fancy math term that means we can pick any two different points in a smaller subset of a bigger space, and they will always have different names.