bloodhound

thats weird. so -126 is not that cold after all!!

huh? i always thought that Celsius was a linear scale?

well, don't know about matt, but i definitely couldn't. cos a 5 year old wouldn't have enough foundation on basic mathematics.

so why dont YOU explain to us (assuming that we are 5 years old ) Why f(x)=x is not a bijection.

what kind of question is that????

looks like he has now

a bijection is a mapping which is both injective and surjective.

a map is injective iff

f(a)=f(b) implies a = b

a map is surjective iff

for all x in the Target there is a y in the Source which is mapped into x by the map

huh? are u saying calculus was invented in a few years. the foundations of calculus was founded well before newton or leibniz were ever born, same can be said to any old theorem.

edit:and the calculus that we now know of took several centuries to develop

is that u in the avatar? if it is, then let me compliment on you beautiful face and hair.

I meant when Andrew Wiles started working on it and finish it.....

many things can be accomplished in ten years. fermats last theorem was proved in ten years. etc.

i wonder if ur a fluid mechanics specialist. if not then are u interested in bodily fluids?

i can't remember what book i read by michael crichton.... it was something about an alien virus which ate humans from inside out turning them into rubbish.... it basically happens is a ship, where they are performing experiments, but due to the lack of gravity, strange form of things leak into the sthip.....

at a similar point in time you say!! theres more than 10 years in difference.......

i think its something to do with the quantisation of energy packets.

yes but newton did it first and did it BETTER...

That doesn't change either of the facts that it was replicated' date=' and this comparison is rather silly.

 

 

 

Most excellent![/quote']

 

replicated by libniz AFTER newton first invented it... many thousands of students replicate results by newton , gauss, einstain every day. that doesnt mean they are better

I'm having trouble proving the following:

Let [math]G[/math] be a group and let [math]a\in G[/math]. Then

[math]\lambda_{a} \colon G \to G[/math]

[math]g \mapsto ag[/math] defines a bijection

For a group [math]G[/math], the family of bijections [math]\{\lambda_{g} \colon g \in G\}[/math].

The map

[math]\lambda \colon G \to SymG[/math]

[math]g \mapsto \lambda_{g}[/math]

is an injective group homomorphism

i can do the lambda being bijective part. but i can't show the map from G to Sym G defined as above is an injective homomorphism.

I know what is 1-1 and onto' date=' but how you can use it to define the size(s) of collections of infinitely many elements?

 

[/quote']

why are u asking ME? i mean , i was just replying to ur previous statement. i had no intention of defining size of collections of infinitely many elements using a mapping.

No Bloodhound, it is not ovbious at all, please read post #1 to see it for yourself.

well, if you ever bothered to use the Universally acknowledged DEFINITION of a bijection then it should be obvious to you.

isac asimov... classic stuff.

I wanted to get hold of the andromeda strain but can't get it anywhere. i guess i have to buy it.

size of a collection and sum of a collection?

well heres an example

[math]\{\tfrac{1}{n^2} \colon n \in \mathbb{N}\}[/math] ovbiously there is a bijection with [math]\mathbb{N}[/math]

and the sum of the elements of that set is equal to [math]\frac{\pi^2}{6}[/math]

u dirty buggers.

nope.... newtons definition of a fluxion or "derivative " was more rigorous than libniz's. liebniz used the vauge concept of "infinitesimals", while newton had the precise form in terms of limits...

yes lebniz's notation is more superior, but newton has more substance.

whats the deal with mpaa anyway??? whenever a new film comes out, they are always talking about record breaking box office figures for each succesive film... and then they complain about downturn in profit whenever the topic of pircay comes along

yes i knew. but other pple might not!!! EXPLICIT