A Bishop is stronger then a Knight !

I tend to believe it depends on position.

And when there is no Position, such as in the first two Diagrams, the Bishop is by Objectivity Stronger than the Knight.
By Objectivity/Static piece Value, the Bishop is ALWAYS Stronger than a Knight, The Rook is ALWAYS stronger than a Bishop, and the queen is ALWAYS stronger than the Rook.

Of course you can be wayward by saying '' I tend to believe it depends on position. '' BUT THIS IS NOT TRUE.... Considering what the Operating Poster Mentioned.
He didn't Mentioned a Big Nuance like  ' the Position ', no, He Mentioned ' by Objectivity '.

( OMG how do I get rid of this yellow stuff?! Get off me!! )

Really, the reason why a lot of ChessPlayers find the Knight better than the Bishop is rather subjectively based, because the Knight has more of a Romantic ( and Mythological ) background than the Bishop, and because the Knight is a ' PathWalker ', a Piece that has a splendid way of indirect movement, and a Piece that for most people looks more Marvellous, while the Bishops movements are Straightforward, and because the Bishop is generally seen as a less beautiful piece.
Still, we should Keep Objective. The Bishop is better.

One of the Reasons why the Bishop pair is by objectivity better than the Knight Pair, is because the Bishop Pair can never get in each others way, directly!.. in Contrast to the Knight Pair; there may be one best spot for one Knight — The other Knight is redundant.
I just read this in my New Book '' Chess Words of Wisdom '', but I already looted some Knowledge from the Internet before. 

I say all this about Knights, but Technically they are good for me; I am a Closed Position Fan.

* somewhat later because it went out of my head the first Time *

And that's also why in Medieval Battle, Archers are by Objectivity better than Infantery and Cavelry; they have the advantage of being Ranged.
A Knight is a melee Unit whereas the Bishop is a long-Ranged one.

Well done on your original analysis, based on an open board.

What makes you think you know more than people who can actually play chess well?

This: http://en.wikipedia.org/wiki/Chess_piece_relative_value

B=N because a lone bishop due to its color blindness can access only half of the chessboard

2B>2N or B+N because in the B pair the color blindness is compensated

You know what is Fun to do?
A Pure Knight versus Bishop Battle without any other pieces involved.
I let Rybka 2.3.2a 32-bit do this against herself, once. now.  

Here are some facts to consider when comparing the B to the N.

1. To some players and writers, at the start of the game, Knights tend to be stronger than Bishops until the central pawns are removed, then the Bishops will become more powerful. In open games, the side with the Bishops pair tends to enjoy an advantage while in closed games it would be the side with the 2 Knights or with a Knight and either active or good Bishop.
2. A Knight in all reality can reach all 64 squares on the board as a single unit. however, the Bishops must both be on the board to be effective in reaching all 64 squares.
3. Knights need support points (i.e. pawns) and Bishops need access to diagonals (the longer the better).
4. If a Bishop can be relegated to being a defensive piece or limited to one diagonal he controls, then the knight will hold superior.

To demonstrate, this is a position I reached Friday against a friend. I will lightly annotate the position.

sometimes the Knight can be stronger.

Great statement: when you aren't playing chess, the bishop is stronger than the knight.

In these positions despite being material up the stronger side needs a knight instead of a bishop to win these positions!

Actually, this was a untimed OTB game played between my sparring partner and I. He overlooked the secondary line but even still, once Nc5 was played, the game was effectively over regardless. There was a longer continuation that was actually played by White (this was the most efficient as found both by Houdini in a similar post and also by going over the game later.

Place the Black King on f8 and the position is completely changed. The Bishop is allowed to become active and a draw is likely going to come out of the game. Still by the original posting, this should be a -1 towards the Bishop side since the Bishop (objectively speaking I think was the term used or something in that vein) should be superior to the Knight in all respects correct?

Also, if the position is left to be a decent position for the Bishop and the Knight somehow does not go to c5 immediately, if the White King can get to f4 or g5, the game will draw as well.

The needs of the given position should be the basis of determination of a piece's value, not necessarily a subjective analysis based on a couple of open diagrams and for God's sake, wikipedia? I have to fact check about 50% of what I find there and shake my head at the rest most of the time.

To see the merits of both pieces, might I suggest reading, "Dvoretsky's Endgame Manual" for real world answers to this debate? While many may scoff at the posts here, you might believe by reading what is considered perhaps the best book written on endgame theory, practice and technique ever.

'Nuff said?

Nonsense, piece value is relative to activity and as a result fluctuates throughout a game. A rook may control 14 squares in the middle of an empty board but it certainly doesn't in a closed position lacking open files or tied to the defence of a weakness, and may be worth significantly less than a well posted knight.

I am also guessing many do not grasp the concept of proper grammar as well?

I know but it sure is fun!