# What does the 'not equal to' sign mean?

• kinkaid
In summary: Groups are just very abstract objects with a couple of basic properties, and groups are just one very abstract mathematical object that can be studied without any numbers. So you don't have to have numbers to do math.----In summary, the 'not equal to' sign ( =/= ) is used to indicate that two objects are not equivalent. It does not imply any other relationships or equalities, and it is not related to the number 0 in any way. This sign is used in programming and in mathematical contexts, but it also has philosophical implications.
kinkaid
the 'not equal to' sign ( =/= )? If I say, blue =/= red. could you simply say: blue = 0 red? Or: life =/= death... mean life = 0 death? Does the not equal to sign mean merely 'incompatible' or does it mean 0 of the thing =/=?

How do you use that sign?! I may be far off

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kinkaid said:
the 'not equal to' sign ( =/= )? If I say, blue =/= red. could you simply say: blue = 0 red? Or: life =/= death... mean life = 0 death? Does the not equal to sign mean merely 'incompatible' or does it mean 0 of the thing =/=?

How do you use that sign?! I may be far off

It simply means that the two objects are not equivalent. It is not valid to derive any equalities from that statement. For example, 2 $\ne$ 3 does not imply that 2 = 0*3 = 0.

then what is the 'not equal to' sign used for. Progamming?

And not equal to what? What if i had a statement blue =/= red... pretty much means blue and red are logically incompatible. Almost like there is 0 red in blue and 0 blue in red. But that's not the function of Not equal to? Not equal to is only 'not equivalent'?

don't forget my question above.

Sometimes it's just as useful to know two things are not equal as it is to know two things are equal.

- Warren

kinkaid said:
the 'not equal to' sign ( =/= )? If I say, blue =/= red. could you simply say: blue = 0 red? Or: life =/= death... mean life = 0 death? Does the not equal to sign mean merely 'incompatible' or does it mean 0 of the thing =/=?

It means "not equal", not "incomparable". 2 is comparable to 3 (in particular, 2 < 3), but they aren't equal. Incomparable things should be not equal -- as in apple =/= 7 -- but then again maybe not... aleph_1 is incomparable to beth_1 in ZFC, but the statement that aleph_1 =/= beth_1 can't be proven in ZFC (since aleph_1 is equal to beth_1 in some models of ZFC, namely those with the continuum hypothesis).

The expression "blue =/= red" is basically shorthand for "it is not the case that blue=red." You can draw no other conclusions from it.

The "not equal sign" isn't really used in the context you are trying to use it for.. saying blue does not equal read is not same as blue equals zero red. It's actually means literally "not equal" as in two things are not equal to each other. You are attempting to over analyze the meaning.

This may be too philosophical for this forum. contextually there is 0 so it has actual math. But I believe the idea is out of mathematical context, more philosophical.

1) 'not equal to' = no (ex. not equal to blue = no blue)
2) no blue = 0 blue
3) therefore, 0 = 'not equal to'

kinkaid said:
This may be too philosophical for this forum. contextually there is 0 so it has actual math. But I believe the idea is out of mathematical context, more philosophical.

1) 'not equal to' = no (ex. not equal to blue = no blue)
2) no blue = 0 blue
3) therefore, 0 = 'not equal to'

Would you say that purple =/= blue?

If so, then purple = 0 blue?

This simply is not true, purple is made of blue and red, so it must have some blue in it right?

Not equal to in no way implies zero of something or zero in anyway. It just means that two objects are not the same exact thing. I think Manchot hit the nail on the head with his definition, you can not draw any other conclusions.

diffy, this may be hard for you. but it either equals blue or it does NOT equal blue. There's no inbetween.

Ad hominem. I see no problem with Diffy's reply.

kinkaid said:
diffy, this may be hard for you. but it either equals blue or it does NOT equal blue. There's no inbetween.

Thanks for insulting me, that's fantastic.

There is no relationship between the 'does not equals sign', and the number 0.

kinkaid said:
If I say, blue =/= red. could you simply say: blue = 0 red?

You can't say that, I'll go for reductio ad absurdum this time. Because then Green =/= red would imply that Green = 0 Red by the same logic. So now we have Blue = 0 Red, and Green = 0 Red, so by transitive Blue = Green.

To be honest, I have no idea what kinkaid is trying to do with the number 0 and $$\neq$$, but it reminds me a bit of how some programming languages such as C/C++ and Perl treat true and false.

In C/C++ and Perl, a true comparison is assigned the number 1 and a false comparison is assigned the number 0 (and any other integer is also consider false). However, it doesn't change anything inside of the comparison at all, it assigns the number to the entire comparison.

I.e, (A != B) is either 0 or 1 (depending on whether it's false or true respectively). This also has no mathematical basis; true and false cannot be considered integers. It is just how the results of operations are stored in memory, and giving the programmer access to this let's him do a few tricks to optimize the program.

But I've never before seen anyone get confused by this and think that this treatment of true and false had any mathematical relevance.

----

kinkaid, you said "it has 0 so it has actual math". However, you don't need numbers to do math. There are in fact a lot of branches of mathematics that don't have any numbers in the basic theory at all and don't depend on the existence of numbers as we usually think of them in any way. For instance, look up http://en.wikipedia.org/wiki/Group_theory" . While some familiar sets of numbers form groups, so do a lot of things that have no numbers in them at all.

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## 1. What does the 'not equal to' sign mean?

The 'not equal to' sign, also known as the inequality sign, is a mathematical symbol used to indicate that two values or expressions are not equal. It is represented by the symbol ≠ and is the opposite of the equal sign (=).

## 2. How is the 'not equal to' sign different from the 'equal to' sign?

The 'not equal to' sign indicates that two values or expressions are not equal, while the 'equal to' sign indicates that they are equal. The 'not equal to' sign is represented by ≠, while the 'equal to' sign is represented by =.

## 3. Can the 'not equal to' sign be used in other contexts besides mathematics?

Yes, the 'not equal to' sign can also be used in programming languages, such as Java and Python, to compare values and determine if they are not equal. It can also be used in logic and other fields to indicate inequality.

## 4. Is the 'not equal to' sign the only symbol used to indicate inequality?

No, there are other symbols used to indicate inequality, such as the greater than (>) and less than (<) signs. However, the 'not equal to' sign is the most commonly used symbol to indicate inequality in mathematics.

## 5. Are there any rules for using the 'not equal to' sign in equations?

Yes, the 'not equal to' sign should always be placed between the two values or expressions that are being compared. It should also be read as "not equal to" or "is not equal to", rather than "not equals". For example, 4 ≠ 5 should be read as "4 is not equal to 5".

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