That's because you are not following the rules!
It would be like me saying,
1 + 1 = 2 + 0
but
2 + 2 = 5 - 1
And then declaring that I have shown something smells fishy.
In reality, however, you have established a false opposition. It is not as if
-1^2 = -1 + 2
in...
You can also use MS-Word. Go to insert, object, Microsoft Equation 3.0, and an equation toolbar will appear.
Also, you can update this toolbar by goint to:
http://www.mathtype.com/msee
And that supports LaTeX.
Zurtex, what software did you use to get this answer, because it seems right that the answer would end in a two, as per Viet Dao's reply? Yet, your software has it ending in five zeros! To help validate your answer, calculate the two parts before you add them, inspect the last digits on each...
Yes! Exactly! And with this we are free to muse about the integral on its own terms -- it is its own thing. Which allosws us to ask the question: what is zero growing into as we add zero to it?
Such a question is a geometric-like way of thinking of the integral. And, as such, no one needs...
Let's start with a simple example. Car squared is not a car that is exponentially bigger. If we apply the idea of squaring to non integers (in this case a car), what do we get? We get gibberish, that's what we get!
Likewise, when we take something to a fractional power, like x to the 1.345...
Let's back up again and think about what it means to take a thing to a power.
Normally, we might think of repeated multiplication when we think of taking something to a power. But there is another way we can think of this. Taking something to a power it a mapping function.
If we only...
Yes, I just realized that we have to add four more! Why? Because in 20 steps, there are four times that five is reduplicated.
Finding the number of times 5 is a prime factor is right, but, for example, when we get to 25 it is in there twice. And so 20 / 5 is 4. There are four times that...
Your question is the same as finding out how often 5 is a prime factor on the natural numbers.
So I am guessing that 100! has 20 zeros, because in counting by fives, we get to 100 after 20 steps.
I am thinking of a famous formula related to number theory, but I have reworded it (this may not be original to me -- I don't know). Can you name the theorm:
If a, b, c and n are positive integers, then
a^{n}=\int_{b}^{c}n{x^{n-1}}dx
has no solutions for any n > 2 . Maybe we can...
It may help to back-up a few steps and ask a different question. Namely, what does it mean to raise anything to a complex number? That is, forget for a moment about e and pi related to i. Think instead: What is it to take a thing to the i power? Before we can answer that, we need to figure...
I like MathCad. If you don't have a package like that, try this:
http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/grapher.html
I am not a heavy Excel user, but I would guess there are plenty of ways to graph in it. And, I would think one could get an add-on package if there is not a...
What kind of computer? What OS? Details!
If you want to write software that runs on an embedded chip and interacts with hardware devices, Check out BASIC Stamp -- which can be bought at Radio Shack. The starting kit is under $100.00. You can hook motors up to this kit as it is extendible...
Yes, and as I think of it, population counting would easily make myriad a useful word to have around! Even theater seating in the Roman world would measure in the myriads. At Pompeii, the theater held two myriad.
This is beyond the original question, but it is interesting to think about the...