Algebraic Topology...

[YoungD]

I almost put this thread under sex and relationships...
Anyway the late Hon. George Saitoti did his PhD in 1973 focusing on Algebraic Topology, now even with the help of diagrams I cannot comprehend what this is/should be used for/has ever been used for/will ever be used for. Does any senator have a clue what this sorcery is??

 

[emali]

Does any senator have a clue what this sorcery is??



 

[Ubongo]

Beyond me and many more...

 

[Ramiran]

Around 1972,73 the late Hon G. Saitoti was a regular customer at 680 PUB so (loops & spaces) describes a highly mathematical procedure to go from the 680 Pub to Koinange street (k-theory)

 

[Aviator]

Does any senator have a clue what this sorcery is??

For illustration purposes only.
Let y=2x+z
And x=3a+b

Algebraic Topology would be used to substitute x in equation (2) as into equation (1).
Like y=2(3a+b)+z
=6a+2b+z.
Now, further from that, you have to study the commutative properties of the equations, since sometimes a+b may not necessarily equal to b+a.

 

[YoungD]

For illustration purposes only.
Let y=2x+z
And x=3a+b

Algebraic Topology would be used to substitute x in equation (2) as into equation (1).
Like y=2(3a+b)+z
=6a+2b+z.
Now, further from that, you have to study the commutative properties of the equations, since sometimes a+b may not necessarily equal to b+a.

 

[MbitikaZetu]

Just skip

 

[bollingo]

Let me begin from the basic,
Suppose R={i, -i, 1, -1} is a given set and define normal multiplication as the binary operation between any two elements of the set, then the set forms a group with the binary operation defined.
Group is closed, all elements are multiplied to get an element in the set
Group is associative, 1*-1=-1*1
Group has an identity element which is 1, 1*i=i ....
This is the basic information about all what he did. Tu comprends?

 

[It's Me Scumbag]

For illustration purposes only.
Let y=2x+z
And x=3a+b

Algebraic Topology would be used to substitute x in equation (2) as into equation (1).
Like y=2(3a+b)+z
=6a+2b+z.
Now, further from that, you have to study the commutative properties of the equations, since sometimes a+b may not necessarily equal to b+a.

since sometimes a+b may not necessarily equal to b+a.

How now? 1+2=3,halafu unasema 2+1=21?
Wueh...

Hesabu za Abbot & Costello hizo nanii...

 

[bollingo]

since sometimes a+b may not necessarily equal to b+a.

How now? 1+2=3,halafu unasema 2+1=21?
Wueh...

Hesabu za Abbot & Costello hizo nanii...

We talk about a binary operation msee.
1-2=-1, 2-1=1. -1 & 1are two different elements, comprends tu?

 

[It's Me Scumbag]

We talk about a binary operation msee.
1-2=-1, 2-1=1. -1 & 1are two different elements, comprends tu?

Now you introduce minus...sorcery as the OP said.

 

[Burner]

We talk about a binary operation msee.
1-2=-1, 2-1=1. -1 & 1are two different elements, comprends tu?

That is not the same. you have changed the value of b in this instance for -2 to +2

 

[bollingo]

Now you introduce minus...sorcery as the OP said.

To demonstrate to you that binary operation can result to two different values using the same initial values. BTW, minus ain't a binary operation.

 

[bollingo]

That is not the same. you have changed the value of b in this instance for -2 to +2

For demonstration purposes. You know this is graduate mathematics, assuming that you know all about algebra, that is the basics, then I can say that a*b may not necessarily be equal to b*a, and you understand.

 

[Burner]

For demonstration purposes. You know this is graduate mathematics, assuming that you know all about algebra, that is the basics, then I can say that a*b may not necessarily be equal to b*a, and you understand.

Wouldnt this (and even in the earlier expression) only apply in the case where either unknown has more than one value e.g if b = √4?

Edit:
Actually i dont believe it matters and i take it back. Whatever the value is for any unknown and no matter how you arrange the expression it must be the same.
@It's Me Scumbag is right. a+b must necessarily be the same as b+a in the same equation.
And a*b=b*a

 

[Aviator]

since sometimes a+b may not necessarily equal to b+a.

How now? 1+2=3,halafu unasema 2+1=21?
Wueh...

Hesabu za Abbot & Costello hizo nanii...

If you travel 10kms north of Nairobi and someone travels 10kms south of Nairobi, do you end up at the same place? No.
Commutative laws don't always apply in nonlinear algebra.

 

[bollingo]

If you travel 10kms north of Nairobi and someone travels 10kms south of Nairobi, do you end up at the same place? No.
Commutative laws don't always apply in nonlinear algebra.

You are right, besides not all binary operations are commutative. In fact, not all groups are commutative.
Just a clarification, what is nonlinear algebra?

 

[Aviator]

what is nonlinear algebra?

Linear algebra is basically arithmetic. Called linear coz a plot of such algebraic function is a line.
Nonlinear algebra is algebra outside this. For example roots and powers, logs and antilogs, complex numbers, etc.

 

[Burner]

You are right, besides not all binary operations are commutative. In fact, not all groups are commutative.
Just a clarification, what is nonlinear algebra?

Besides nonlinear algebra, where else would this be the case? I cant think of any example.

 

[bollingo]

Besides nonlinear algebra, where else would this be the case? I cant think of any example.

Outside nonlinear algebra, it will be less relevant.