What happens when you apply this theory to how I like my bacon cooked?
Does it come out
Just done
Crispy
Very crispy
Burnt
Thanks.
Does it come out
Just done
Crispy
Very crispy
Burnt
Thanks.
can you count with the complex numbers? Let us say?
If I say I have 3 Apples. What does it mean to have i apple?
If I say I have 3 Apples. What does it mean to have i apple?
"Counting" is done by establishing a one-to-one correspondence between the things to be counted and the positive integers, {1, 2, 3, 4, 5 ....}.
At this point, I'd say no, one may not "count with the complex numbers." BUT ....
we must be careful. We may not count with "the" complex numbers (meaning all of them), but we may indeed count with SOME of them!
Which ones?
1 + 0i
2 + 0i
3 + 0i
4 + 0i
5 + 0i
and so forth.
Because THESE particular complex numbers are equivalent to positive integers wearing a different shirt. So to speak.
They are, however, just a tiny portion of all the complex numbers available for our enjoyment.
Complex numbers are lovely. Yet not so lovely as the hippopotamus opening, which is lovelier still!
Edit: I suspect, however, that the real question asked is: "is i a number that really makes any sense?"
The answer to that is: Yes, the number "i" makes plenty of sense.
It stands for the square root of negative one -- and, as I hope we all know -- taking the square root of a negative number yields no answer among the "real" numbers (in either sense of the adjective real).
BUT, as sneaky mathematicians tend to do, we can claim that "i" makes sense ANYWAY. How so?
Well, let's write "i" wearing all its real number clothes: 0 + 1 i
THAT number (equivalent to "i") can be graphed in two dimensions!
On the x-axis we install a real number scale that extends in both directions, left and right.
On the y-axis, we install a real number scale that extends up and down, but means the real number of "i" s that we have! 1 i, 2 i's, 3 i's, 4 i's, 5 i's, and so forth.
Where the two axes intersect -- at the graph's "origin" -- we can find the complex number 0 + 0 i.
NOW, to graph the complex number "i" (which is equivalent to 0 + 1 i), we just start at the origin of the graph and then shift right "0" units (which is not at all), and shift up "1" unit. On the graph, of course. And POP, draw a point right there.
Suddenly, "i" makes plenty of sense! It's sitting right there! It's a geometrical thing, for real! We can see it as a little point on the two-dimensional plane!
If we want to, we can even draw a little arrow that goes from the origin of the graph straight up to where "i" is living! And we can call that arrow (it's the graphical representation of a vector) the number "i" too, if we want. And we can see it even more clearly!
Its a lovely thing! Just not as lovely as the hippopotamus opening.
At this point, I'd say no, one may not "count with the complex numbers." BUT ....
we must be careful. We may not count with "the" complex numbers (meaning all of them), but we may indeed count with SOME of them!
Which ones?
1 + 0i
2 + 0i
3 + 0i
4 + 0i
5 + 0i
and so forth.
Because THESE particular complex numbers are equivalent to positive integers wearing a different shirt. So to speak.
They are, however, just a tiny portion of all the complex numbers available for our enjoyment.
Complex numbers are lovely. Yet not so lovely as the hippopotamus opening, which is lovelier still!
Edit: I suspect, however, that the real question asked is: "is i a number that really makes any sense?"
The answer to that is: Yes, the number "i" makes plenty of sense.
It stands for the square root of negative one -- and, as I hope we all know -- taking the square root of a negative number yields no answer among the "real" numbers (in either sense of the adjective real).
BUT, as sneaky mathematicians tend to do, we can claim that "i" makes sense ANYWAY. How so?
Well, let's write "i" wearing all its real number clothes: 0 + 1 i
THAT number (equivalent to "i") can be graphed in two dimensions!
On the x-axis we install a real number scale that extends in both directions, left and right.
On the y-axis, we install a real number scale that extends up and down, but means the real number of "i" s that we have! 1 i, 2 i's, 3 i's, 4 i's, 5 i's, and so forth.
Where the two axes intersect -- at the graph's "origin" -- we can find the complex number 0 + 0 i.
NOW, to graph the complex number "i" (which is equivalent to 0 + 1 i), we just start at the origin of the graph and then shift right "0" units (which is not at all), and shift up "1" unit. On the graph, of course. And POP, draw a point right there.
Suddenly, "i" makes plenty of sense! It's sitting right there! It's a geometrical thing, for real! We can see it as a little point on the two-dimensional plane!
If we want to, we can even draw a little arrow that goes from the origin of the graph straight up to where "i" is living! And we can call that arrow (it's the graphical representation of a vector) the number "i" too, if we want. And we can see it even more clearly!
Its a lovely thing! Just not as lovely as the hippopotamus opening.
i equals also e to the power of (i times half pi)
My bacon is still sat waiting to be cooked and I’m bloody hungry! How can I use this to cook my bacon perfectly?
Were it not for complex numbers, GPS could not work to guide your bacon across the skies or down the highways, Boris.
And I, too, am a fan of bacon. So long as it's not hippopotamus bacon. That, I could not recommend.
And I, too, am a fan of bacon. So long as it's not hippopotamus bacon. That, I could not recommend.
@Noflaps Good bacon already knows the coordinates to my grill. I don’t think I’d be a fan of hippo bacon though.. those teeth are way to dangerous.
e^(i * pi) + 1 = 0. Gaze in wonder at that, as Euler no doubt did when he discovered it, long ago. (* = multiplication)
so, even more oddly: e^(i * pi) = -1
And yet some think there is no God. Snicker.
so, even more oddly: e^(i * pi) = -1
And yet some think there is no God. Snicker.