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Is zero really a number?
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You are currently reading a thread in /sci/ - Science & Math

for a long time my teachers have hammered into my brain that
infinity is not a number, it's just a concept. Now that I understand
that, I wonder if zero is just a concept too? I guess this is both a
philosophical and a mathematical question.

Philosophically, you can't really have a zero of things, because the
thing which is zero doesn't really exist. In fact, if you do count
things that don't really exist, you will have an infinite number of
those things since there is no limit to things that you can imagine
existing (which is rather an interesting fact).

In mathematics, many definitions and rules go haywire when they try
to deal with zero (such as 0^0, 1/0, 0/0). The two most used bounds
for evaluating the limit of a function are in fact 0 and infinity.

So it seems obvious that there is a deep intricate relation between
zero and infinity. And like infinity, it seems that zero should just
be considered a concept. Furthermore, by making zero a concept we
would be able to avoid writing those exceptions to rules where we have
to specify that the equation is true as long as something is not zero.

I just thought of few more examples:

1) If in a game, your opponent has 1 point and you have two points
then you can say that you have twice as many points as him. Whereas
if your opponent has zero points and you have two points, you would
technically have to say that you have infinite times as many points
as him.
2) You can't really have a circle with radius zero.
3) Zero is neither positive nor negative and neither it is even or odd.
>>
Philosophically, almost anything is a concept. The difference in the concrete case is semantics. What your teacher meant is that infinity is not a number in the sense that is not an element of the set of reals (technical math babble); if you draw a number line, you can never reach infinity, but any finite number can in theory be reached (even stupendously large ones). In this sense zero is a number and infinity is not.

While you are right that zero and infinity are very much related, your wording does not make a lot of sense. "By making zero a concept" has no meaning in the mathematical sense, nor does it in the philosophical one.

1) That's ratio's for you.
2) You can, since technically, a circle is defined to be the set of points that have a distance equal to the radius from a certain center point. If this distance is zero, then this set reduces to the set with just the center point in it. (Aka, a point.)
3) I'm not sure what you're aiming at with this one. Besides that zero is quite definitely even.
>>
>he thinks math isn't a concept
>>
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2 MB, 2856x1513
>>7649720
>>7649723

Please do not reply to the spam bot. It crawls for various shitty threads and reposts them by random in order to lower the quality of this board.

http://mathforum.org/library/drmath/view/68357.html
>>
>>7649728
lol I'm not a spam bot.

OP here. I just happened to have this thought about zero, did a quick google search, and pasted the first interesting question I found related to it onto this board.

The reason why I did it is simple. I wanted to see what you guys would say.

>>
>>7649730

>lol I'm not a spam bot.

yeah that's what a spambot would say, typical just typical
>>
>>7649730
So if you think zero isn't a number, then what about irrational numbers? They don't really exist either. Nor do imaginary numbers. In fact, even the basic numbers do not exist. 3 is not real. You may counter "but I can have 3 of an object!" However, what you really have is 1 group of objects which you arbitrarily ascribed an abstract concept onto.
>>
>>7649748
Nigga I'm not here to actually debate whether or not zero is a number. I literally drank a few beers, had a thought in my head, and pasted someone else's words onto 4chan to see what y'all would say. It's all just for fun here. I'm not really trying to prove a point.
>>
>>7649708
Zero has many properties that numbers have. It has a parity, for example
>>
>>7649748
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>>7649894
By OP's own definitions there can not be zero spam bots in this thread.
>>7649708
Zero was invented by the Arabs in the 17th Century I believe, to make accounting easier.