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### Course: Algebra 1>Unit 1

Lesson 1: Overview and history of algebra

# Abstract-ness

Abstraction is like taking a real thing and turning it into an idea. We can use a cube as an example. Even though cubes can look different in real life, the abstract idea of what a cube is stays the same. Created by Sal Khan.

## Want to join the conversation?

• At Sal said that in reality there is no perfect cube. Is there any perfect 3-dimensional objects in reality (ex. perfect spheres, perfect cubes, perfect rectangular prisms, perfect pyramids, etc.)?
• In the real world, we also have something like "spacetime", which is sometimes seen as the fourth dimension. In mathematical abstracts, even solid figures are represented without any specific reference to spacetime. Due to that, there cannot exist any ideal "cube" for example. Any real cube will include some aspects and features that are specific to them. That's a philosophical problem as well.
• Wait, why is Sal talking about Geometry at ? I thought this was an Algebra class...
,:\
• While algebra has to do with equations and formulas, geometry has to do with objects and shape. It may not seem like they're related, but they actually are.

Take y = x as an example. This equation can be graphed so that it creates a set of point that turn into a straight line. An equation, an algebraic concept, can be graphed so that it becomes a geometric concept!

Another example would be the Pythagorean Theorem (a^2 + b^2 = c^2), a theorem that states if the legs of length "a" and "b" are of a right triangle then it's hypotenuse would be of length "c". Here, the side lengths of a right triangle (a geometric concept) can be then related to an equation (a algebraic concept).
• How and why is algebra so abstract?
• Something that is abstract is something that exists in your thoughts and your mind but is not a physical object. That said, algebra is abstract because numbers are a man-made metaphysical construct used to do mathematics.
• to wrap up:
Abstract is Abstract
• Thnx 4 making it so Simple LOL
• what is the purpose of making about video Abstract-ness? Is really helpful in learning algebra?
• Up until now, you have been working with specific numbers as you learn basic arithmetic. In algebra, you will be using variables to generalize calculations or to represent unknown values. You won't know what number the variables represent. This is where the abstraction come in. You will learn how to simplify algebraic expressions to the extent possible even though you don't know the value of the variables.
• i dont understand the comparison between abstractness and real world and reality, when the definition of abstract is theoretical ideal or theory. My question is why would we base our devoted time and brain capacity for something we still have yet to prove its signfigance to our everyday life and prove further from theory?
• Abstraction is studied as it's the process of compressing information in our brain to make room for more concepts. Imagine how much devoted time and brain capacity would have to be wasted if we were to remember every single pointless minute detail of every math problem.

Instead, we develop theories, equations, formulas that can be applied to multiple instances of math. Imagine how difficult it would be to remember the quantity of every single object if we were not to use a numerical symbol to represent it such as 1, 2 or 3. Imagine how much time we'd waste pointing at various objects to try to convey an idea rather than saying abstract words that represent them instead such as "wood", "stone", "food", etc.
• i am curious that what mathematical rules or concepts are taken from early mathematicians ?
• Apoorva, all of math is derived from the foundational basics. It is absolutely essential that you understand the foundational concepts to build on the higher mathematical rules a head.
• Would this be considered a good definition of "abstract:"
"Abstract: considered apart from concrete existence."?