Normed space
Okay kiddo, so a normed space is a special kind of space where we can measure how long or big something is. Just like how we measure the length of a pencil, we can measure the length or size of things in this kind of space.
In a normed space, we use something called a "norm" to measure the size of things. A norm is basically like a ruler that we use to measure the length of a pencil. We use it to measure the size of things in the space.
Now, this space is a bit special because it follows some rules that other spaces don't. For example, if we have two things in the space, we can add them together and the result will still be in the space. Think of it like putting two pencils together to make a longer pencil.
Another thing that makes this space special is that we can multiply things in the space by a number (like multiplying a pencil's length by 2). This also follows some rules that other spaces might not follow.
Overall, a normed space is a space where we can measure sizes of things using a norm, and where things follow some special rules when we add them together or multiply them by numbers.
In a normed space, we use something called a "norm" to measure the size of things. A norm is basically like a ruler that we use to measure the length of a pencil. We use it to measure the size of things in the space.
Now, this space is a bit special because it follows some rules that other spaces don't. For example, if we have two things in the space, we can add them together and the result will still be in the space. Think of it like putting two pencils together to make a longer pencil.
Another thing that makes this space special is that we can multiply things in the space by a number (like multiplying a pencil's length by 2). This also follows some rules that other spaces might not follow.
Overall, a normed space is a space where we can measure sizes of things using a norm, and where things follow some special rules when we add them together or multiply them by numbers.
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