Proper base change theorem
The proper base change theorem is like a special rule in math that helps us switch the order of two operations. It's like when you have a toy with different pieces, and you want to change the way you put the pieces together.
Imagine you have two different ways of doing math problems. The first way is called "base change," and the second way is called "pullback." Each of these ways has its own set of rules and steps to follow.
The base change way is like using one set of toys to build something, like using Legos to build a house. You have all the Lego pieces and instructions on how to use them. But sometimes, you might want to switch to using a different set of toys, like using wooden blocks to build the same house. The proper base change theorem tells you that if you follow the instructions for the Lego set and then switch to the wooden blocks, your house will still look the same. It means that the order of the steps doesn't matter; you can switch the toys and still get the same result.
The pullback way is like using a different set of instructions to build the same thing. It's like if you had two sets of Lego instructions for building the same house. But what if you didn't have the Legos or the wooden blocks? The pullback way tells you that you can use the instructions from the Lego set to build the house with the wooden blocks. It means that even if you don't have the exact same toys or instructions, you can still get the same result by using a different way.
The proper base change theorem is just a fancy name for saying that you can switch the toys or the instructions and still get the same result. It helps mathematicians solve problems in a different way if they have different tools or instructions. Whether we change the toys or the instructions, the end result will be the same.
Imagine you have two different ways of doing math problems. The first way is called "base change," and the second way is called "pullback." Each of these ways has its own set of rules and steps to follow.
The base change way is like using one set of toys to build something, like using Legos to build a house. You have all the Lego pieces and instructions on how to use them. But sometimes, you might want to switch to using a different set of toys, like using wooden blocks to build the same house. The proper base change theorem tells you that if you follow the instructions for the Lego set and then switch to the wooden blocks, your house will still look the same. It means that the order of the steps doesn't matter; you can switch the toys and still get the same result.
The pullback way is like using a different set of instructions to build the same thing. It's like if you had two sets of Lego instructions for building the same house. But what if you didn't have the Legos or the wooden blocks? The pullback way tells you that you can use the instructions from the Lego set to build the house with the wooden blocks. It means that even if you don't have the exact same toys or instructions, you can still get the same result by using a different way.
The proper base change theorem is just a fancy name for saying that you can switch the toys or the instructions and still get the same result. It helps mathematicians solve problems in a different way if they have different tools or instructions. Whether we change the toys or the instructions, the end result will be the same.