Can Mathematical Induction Prove the Existence of a Fourth Dimension?

[PTiger]

I am currently exploring if whether or not a fourth dimension exists or can be drawn. According to my professor, I have to use mathematical induction.


I know that 2^n is the equation and "n" equals the dimension. Therefore 2^1 is 2. The first dimension is a line with 2 terminal points and 2^2 =4 because the second dimension is four terminal points.

For mathematical induction, I guess I'm trying to prove that 2^n is true and 2^n+1. The only way I can prove this is by drawing it. I can draw that 2^4 = 16 terminal points and 2^n+1, I can show that you can end up with 4 terminal points, 16 terminal points...However, I don't know what type of equation to use.

 

[Ray Vickson]

I am currently exploring if whether or not a fourth dimension exists or can be drawn. According to my professor, I have to use mathematical induction.


I know that 2^n is the equation and "n" equals the dimension. Therefore 2^1 is 2. The first dimension is a line with 2 terminal points and 2^2 =4 because the second dimension is four terminal points.

For mathematical induction, I guess I'm trying to prove that 2^n is true and 2^n+1. The only way I can prove this is by drawing it. I can draw that 2^4 = 16 terminal points and 2^n+1, I can show that you can end up with 4 terminal points, 16 terminal points...However, I don't know what type of equation to use.

You need to use parentheses to make your expressions clear. For example, 2^4+1 = 16+1 = 17 when read using standard rules, but 2^(4+1) = 2^5 = 32. If you mean 2^(4+1), you need to write it like that, or else use the "superscript" button (on the pallette at the top of the input pane---it looks like X²); that would give you 2⁴⁺¹.

RGV

 

[Mark44]

I am currently exploring if whether or not a fourth dimension exists or can be drawn. According to my professor, I have to use mathematical induction.


I know that 2^n is the equation and "n" equals the dimension. Therefore 2^1 is 2. The first dimension is a line with 2 terminal points and 2^2 =4 because the second dimension is four terminal points.

For mathematical induction, I guess I'm trying to prove that 2^n is true and 2^n+1.

2ⁿ is not a statement, so it's meaningless to say that it is either true or false. Same with 2ⁿ⁺¹.

Examples of statements:
x + 1 = 3
y < 5
The name of my dog is Dylan.

Regarding the problem you posted, I don't believe that you have described it correctly. Induction proofs are not used to prove statements about specific value of n, such as n = 4. They are used to proved statements of a more general statement.

What exactly are you trying to prove?

The only way I can prove this is by drawing it. I can draw that 2^4 = 16 terminal points and 2^n+1, I can show that you can end up with 4 terminal points, 16 terminal points...However, I don't know what type of equation to use.

 

[Punkyc7]

Assume that the statement holds for n=1,...n and show that it implies true for n+1