The Instigator
TheAwesomeRuler
Con (against)
Losing
7 Points
The Contender
KingDebater
Pro (for)
Winning
11 Points

Why 0 to the power of 0 is 1 or anything to the power of 0 is 1

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Post Voting Period
The voting period for this debate has ended.
after 4 votes the winner is...
KingDebater
Voting Style: Open Point System: 7 Point
Started: 4/4/2013 Category: Science
Updated: 4 years ago Status: Post Voting Period
Viewed: 1,132 times Debate No: 32079
Debate Rounds (5)
Comments (5)
Votes (4)

 

TheAwesomeRuler

Con

Why is 0 to the power of 1 or anything to the power of 0 is 1
The 1st round is acceptance
Best Of Luck Contender
KingDebater

Pro

I accept.
I quite like maths but haven't been in a real debate about maths yet, so this should be interesting.
Debate Round No. 1
TheAwesomeRuler

Con

Well as we all know maths anything Times 0 gives us 0. Ever come to think of it that 0 stands for nothing and nor can we also divide anything by zero as it gives us an undefined number which can be anything from -x to +infinite.
When we power any number by 0 as we know that zero times any number gives us zero so shouldn't nothing to the power of nothing give us nothing and what is the explanation that it gives us one. Is there a formula because i have looked and questioned every single good mathematician but he dose not know.
Hope you can answer this..
KingDebater

Pro

Con's argument about nothing being multiplied by nothing is irrelevant. Let's take 2 to the power of 2, for example. We know that this is 4 as 2*2=4. Now let's try to work out 2 to the power of 1. We knw this to be 2. What is the difference between 2 to the power of 1 and 2 to the power of 2? Well, to go up in the sequence we multiply by two, and to go down in the sequence, we divide by two. So now, we need to go down in the sequence from 2 to the power of 1 to 2 to the power of zero. 2 divided by 2 equals 1 and so we come to the conclusion that two to the power of zero is one.

X to the power of 1 = X
X to the power of 0 = X to the power of 1 divided by X
X divided by X = 1
Therefore, X to the power of 0 = 1

I hope that answered your question.

Vote Pro.
Debate Round No. 2
TheAwesomeRuler

Con

Though here I am not talking about the minus rule when a divide is applied on a indice. I am generalising the fact that without any number and I am giving you only one number 0. I hereby ask you now directly why is 0 to the power of 0 one without dividing it.
0 to the power of 0 is
0*0
and 0*0 =0
Another example:
5*0*0(this can go on forever)
=0
Hereby I have answered you flaw in argument

And I am sorry to say but you have not answered my question you have given an example on Exponentiationlisation and thus hereby have you not given nor answered my debate.
Vote Con
KingDebater

Pro

That's not the point, though. If we are to find the answer, we will have to work through the pattern. If X to the power of 1 is X and to go back in the sequence we divide by X and X divided by X is 1, then it follows logically that any number to the power of 0 is 1. To deny the conclusion, you would have to deny one of the following facts:

1) X to the power of 1 = X
2) To go backwards in the sequence, we divide by X.
3) X divided by X is 1

Again, here is the formulation of the logic behind the fact that anything to the power of 0 is 1 is here:

P1) X^1=X
P2) (X^Y)/X=(X^Y-1)
P3) (X^1)/X=(X^0) (from 2)
P4) X/X=1
C) (X^0)=1 (from 1,3,4)

For my argument to actually be disproved by Con, he will need to either deny the fact that it's a sound syllogism, or that one of the premises is false. So far, he has failed to do this.

Vote Pro.
Debate Round No. 3
TheAwesomeRuler

Con

Here we go again.
I do not want any equations, it is either you are not looking at the question correctly or you are repeating what you said.
As I said 0^0=0*0
=0
just as 5^1=5*1
=5
Here there are no direct equations nor theory, I will not say that this sounds sylloigism or that either of the premises is false though i can say that in maths there are a few questions in which there are more than one answer for example my other debate which I will post shortly will show it 6"2(1 2) = 9 OR 1
KingDebater

Pro

Here is Con's argument:

(P1) X^Y = X*Y
(P2) X^0 = X*0 (from 1)
(P3) X*0=0
(C) Therefore, X^0=0 (from 2,3)

The problem lies in the first premise, as it's not true that X^Y = X*Y. For example, 2^-2= 1/4, as it follows logically when we just divide by two when going back in the sequence.
2^4=16
2^3=8
2^2=4
2^1=2
2^0=1
2^-1=1/2
2^-2=1/4

Am I wrong?
Con says: Here there are no direct equations nor theory, I will not say that this sounds sylloigism or that either of the premises is false though i can say that in maths there are a few questions in which there are more than one answer for example my other debate which I will post shortly will show it 6"2(1 2) = 9 OR 1
Actually, there is only one answer to every maths equation. The equation that Con presents is the following:
6÷2(1+2)
So how do we work this one out? Well, Bidmas states the order in which we work out equations, which states that brackets go first, then indices, then division, then multiplication, then addition, and finally subtraction. So we work it out as follows:
6÷2(1+2)
6÷2*3
3*3=9
Therefore, the answer to the equation that Con presented can only be 9. To say that the answer is one would be a violation of bidmas.
Debate Round No. 4
TheAwesomeRuler

Con

TheAwesomeRuler forfeited this round.
KingDebater

Pro

Vote Pro.
Debate Round No. 5
5 comments have been posted on this debate. Showing 1 through 5 records.
Posted by rottingroom 4 years ago
rottingroom
Exponents are actually a mathematical formula used to determine growth. We only remove (or simplify) the parts that seem practically unnecessary to make the learning process easier. This is acceptable because simplification of the formula works for every situation except in the case of 0^0.

We learn to conceptualize exponents like this:

growth^duration = answer

so it would seem to follow that 0^0 = 0

However, the actual application of this is this:

original * growth^duration = new

or

growth^duration = new/original

The expression "growth^duration=0" does not change the final product. It just means that there was no "growth" and no "duration" of time for growth. Whatever value "new" was when it was "original", it is still that number after the operations. Therefore "0^0 = anything". A calculator considers this but proceeds with the final operation "new/original" which will always be the same number if the operation is 0^0, hence the answer "1".

The answer is anything because when you have something and 0 growth occurs during 0 time you still have what you had at the beginning.

If you have 5 apples and they don"t grow exponentially then how many apples do you have? Hint: It"s not 0 or 1!
Posted by guesswhat101 4 years ago
guesswhat101
Clearly neither of you have ever taken calculus nor have heard of limits
Posted by guesswhat101 4 years ago
guesswhat101
Clearly neither of you have ever taken calculus nor have heard of limits
Posted by rottingroom 4 years ago
rottingroom
you guys are both wrong. I'll wait til the resolution to explain.
Posted by elvroin_vonn_trazem 4 years ago
elvroin_vonn_trazem
Mathematics is not normally a subject of debate, because math statements tend to be provable one way or the other. In this case, zero to the zero power is formally declared to be "undefined". That MAY mean that it is something that can be argued-about....

http://www.math.hmc.edu...
4 votes have been placed for this debate. Showing 1 through 4 records.
Vote Placed by KroneckerDelta 4 years ago
KroneckerDelta
TheAwesomeRulerKingDebaterTied
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Reasons for voting decision: Neither side had any clue what they were talking about. Con's assumption that we say 0^0 = 1 is false and thus Con is the correct side, but they do not properly justify why it is false...merely by mistakenly saying that 0^0 = 0*0. So here's the problem: Pro never refutes Con's question about dividing by 0, but the only argument Con offers is that 0^0 = 0*0 = 0 which Pro correctly states is incorrect.
Vote Placed by Subutai 4 years ago
Subutai
TheAwesomeRulerKingDebaterTied
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Reasons for voting decision: Stop it qopel.
Vote Placed by qopel 4 years ago
qopel
TheAwesomeRulerKingDebaterTied
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Reasons for voting decision: CVB
Vote Placed by lannan13 4 years ago
lannan13
TheAwesomeRulerKingDebaterTied
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Reasons for voting decision: Ff