An unusually easy proof of vector.

In summary, a vector in mathematics is a mathematical object with both magnitude and direction, typically represented by an arrow. This proof of vector is considered easy because it only requires basic concepts and techniques in math, and was first introduced by William Rowan Hamilton in the 19th century. It can be applied to all types of vectors and has various real-world applications in physics and engineering.
  • #1
athrun200
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Homework Statement


See the attachment.


Homework Equations





The Attempt at a Solution



It seems this proof is trivial, too easy that I am not sure if I do it correctly.
 

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  • #2
Yes, it is too trivial

You start by saying [itex]||u||_\infty= |u_n|[/itex]. You can't do that [itex]||u||_\infty[/itex] is the largest component, not necessarily the nth component

You can say [itex]||u||_\infty\le |u_n|[/itex]. Does that help?
 

FAQ: An unusually easy proof of vector.

What is a "vector" in mathematics?

A vector is a mathematical object that has both magnitude (or size) and direction. It is typically represented by an arrow in a coordinate system, with the length of the arrow indicating the magnitude and the direction indicating the direction.

What makes this proof of vector so easy?

This particular proof of vector is considered easy because it requires only basic concepts and techniques in mathematics, such as algebra and geometry. It does not involve complex equations or advanced mathematical concepts.

Who first came up with this proof of vector?

The proof of vector was first introduced by mathematician William Rowan Hamilton in the 19th century. However, there have been various modifications and improvements made to the proof by other mathematicians over time.

Can this proof be applied to all types of vectors?

Yes, this proof can be applied to all types of vectors, including two-dimensional and three-dimensional vectors. It is a general proof that can be used in various mathematical contexts.

How can this proof be used in real-world applications?

The proof of vector has many real-world applications, particularly in physics and engineering. It is used to solve problems involving forces, motion, and direction, such as in the design of structures or the analysis of motion in a physical system.

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