# TED Community » Goran Malic

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##### People don't know that I'm good at

loitering

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• #### A comment onTalk: Andrea Ghez: The hunt for a supermassive black hole

Sep 3 2011: I lose all audio after 9:38. Is anybody else experiencing this problem? Only this video is affected, I tried reloading the page and restarting my browser but no luck so far.
• #### A reply onConversation: Does infinity exist?

Sep 3 2011: No, you couldn't for couple of reasons. The division operation is defined for numbers. Infinity is not a number. If you would try to work with infinity instead of numbers, you would get the following contradiction:

We say that a is divisible by b if there exists c such that a=b*c. If such c exists, it is unique and we say that c is the result of the division of a by b. For example, take a=7 and b=7. We have to find c such that 7=7*c. Obviously, c=1, so the result of division of 7 by 7 is 1.

Now let a=infinity and b=infinity. We have to find c such that infinity=infinity * c.

Obviously c=1. But, c=2 will also do since infinity*2=infinity. And c=3, c=4, c=4392123249543 will also do. Even c=infinity will be OK since infinity*infinity=infinity. So far we have that infinity / infinity = 1 and infinity / infinity = infinity, and by combining this two equalities we conclude that 1=infinity. And that obviously isn't true.
• #### A reply onConversation: Does infinity exist?

Aug 30 2011: When extra dimensions are added infinity actually behaves very politely! In your example, adding another dimension to an infinite two-dimensional space does not produce an infinity to the power of infinity; instead, nothing really happens, infinity remains the same infinity you had in the beginning.

Think of it this way: a circle is a specific set of points contained in a plane, that is, it is a subset of the plane. A sphere is a specific subset of space. How many points are there in a plane? And how many in space? The answer is the same, both have an infinite number of points, so neither the circle nor the sphere can have more than an infinite number of points, i.e. they have exactly an infinite number of points, not infinity to the power of infinity.

Our intuition falls apart when dealing with infinity. A clear example is this one: consider the set of all positive integers 1, 2, 3, 4, 5 and so on. Now, cross out all the odd numbers in this set. You'll get the set consisting of all even integers 2, 4, 6, 8 and so on. The question is: which one is larger, the set of all positive integers or the set of both positive and even integers?

The usual answer is that the set of all positive integers is larger since we obtained the other set by crossing out odd numbers, but actually, they are of the same size, both are infinite. To clarify why this is so: well, we just rearrange the counting pattern of the even integers, we consider 2 as the first even integer, 4 as the second even integer, 6 as the third even integer and so on. In such a way we have established a correspondence in which 2 corresponds to 1, 4 corresponds to 2, 6 corresponds to 3, 8 corresponds to 4, 10 corresponds to 5 and so on, that is, to every even integer we can assign a corresponding integer. From this we conclude that there are as many even integers as there are all of the integers.
• #### A reply onConversation: Does infinity exist?

Aug 28 2011: Numbers are an abstract concept and although they seem natural to us, they are not real phenomena, so the notion of size doesn't really apply to them in the same sense that the notion of sound or color doesn't apply to them (i.e. we cannot say what is the size of 17 in the same way that we cannot say what is the color or sound or smell of 39).

We can, however, discuss the size of a number relative to another number (i.e. 7 is larger than -4 or 0 is greater than -1 etc.) or its absolute value (i.e. its distance on the real line (the x-axis) from the origin) which is usually called the magnitude of a number.
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#### A comment onConversation: Do you think that God created the Universe? If that was the case, how was that supposed to happen?

Aug 26 2011: When talking about a creator, be it a God or a random set of (super)natural entities, you also have to take into consideration that if a God (or a random entity) created the universe, then its actions are not necessarily limited by logic, physics or any kind of reasoning and that it can make and brake the rules on a whim.

So if we conclude that your 6 premises lead to a paradox, it still doesn't disprove the existence of a creator. It could be that in the house on the beach where the creator created our universe some different set of rules and regulations apply.

It's something like a game of chess - chess pieces follow a set of rules imposed by a creator, but outside the chessboard, the creator doesn't have to play according to the rules of chess. Even within the chessboard universe the creators (players) can agree to change the rules just for fun.
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#### A comment onConversation: Does infinity exist?

Aug 26 2011: As it was pointed out earlier, infinity is not a number. More or less mathematically, it is a measure of size of the set of all integers. To be more precise, that is the definition of countable infinity in the sense that we know the successor and the predecessor of every integer, i.e. if we pick an integer "n", we can say that "n-1" is its predecessor and "n+1" is its successor and because of that, we can "count the integers".

As the name "countable infinity" suggests, there is, surprisingly, another kind of infinity called the uncountable infinity. That is the size of the set of all numbers and it is uncountable in the sense that we can no longer find the successor and the predecessor of any number. For example, if we choose 1 and try to find its successor, we could say that 1.00000001 is its successor - but that is not true because 1.000000001 or 1.0000000000000001 or 1.00000000000000000000000000001 (and so on) should be its successor.

As it turns out, the uncountable infinity is interestingly much larger than the countable infinity - although the term "larger" is not a good one; it should be substituted with "denser".

To answer the original question, as far as I know, there is no example of infinity in nature. Even the curved finite spaces such as the area of the Earth are finite in size, and one would eventually walk across every atom on the surface of the Earth.

As for the understanding of infinity, we cannot say that we understand it completely, but we can say that we have made significant progress ever since Georg Cantor inaugurated a branch of mathematics called "set theory" in the 1870s. There are still a lot of unanswered questions and some questions about infinity truly test the limits of mathematics as such - for example, the continuum hypothesis, which states that there is no infinity "more dense" than the countable infinity and "less dense" than the uncountable one, cannot be proved or disproved within the standard mathematical framework.
• #### A reply onConversation: Does infinity exist?

Aug 26 2011: It is not true that infinity cannot be defined properly. It is defined as the cardinality or size of the set of all integers. :) To be more precise, countable infinity is defined as the cardinality of the set of all integers. Uncountable infinity is defined as the cardinality of the set of real numbers.

As for the division by zero example, I wouldn't say that mathematicians like to take it as infinity. They take it as infinity in terms of limits, i.e. when it is possible, "n/0" is replaced with "the limit of n/x as x approaches zero" which indeed is infinity.

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