Dividing by Zero

[Strontium]

1/0=1
1 divided by 0, is 1 divided by nothing.
1 times nothing is nothing 1 time, which is nothing.
1 divided by nothing is 1, because 1 is not divided by anything.
Or am I missing something?

 

[nycmathguy]

1/0=1
1 divided by 0, is 1 divided by nothing.
1 times nothing is nothing 1 time, which is nothing.
1 divided by nothing is 1, because 1 is not divided by anything.
Or am I missing something?

Any number divides by 0 = undefined. Division by zero is not possible.

Sample: 222 ÷ 0 = undefined.

Any number divided by 1 = the number itself.

Sample: 222 ÷ 1 = 222

 

[HallsofIvy]

1/0=1
1 divided by 0, is 1 divided by nothing.
1 times nothing is nothing 1 time, which is nothing.
1 divided by nothing is 1, because 1 is not divided by anything.
Or am I missing something?

That is "handwaving" not mathematics! "Nothing" is NOT a number.
If a/b= c then a= bc. If a/0= c then a= 0c. But 0 times any number is 0.
If a is not 0, there is NO such c. a/0 is "undefined".

If 0/0= c then 0= 0c which is true for any c
We say that 0/0 is "undetermined", not "undefined".

 

[nycmathguy]

That is "handwaving" not mathematics! "Nothing" is NOT a number.
If a/b= c then a= bc. If a/0= c then a= 0c. But 0 times any number is 0.
If a is not 0, there is NO such c. a/0 is "undefined".

If 0/0= c then 0= 0c which is true for any c
We say that 0/0 is "undetermined", not "undefined".

Interesting reply.

 

[conway]

Consider then, that as it stands....

There are an infinite number of expressions that cannot be defined, or answered.

Vertical slopes cannot be defined, yet clearly they are vertical.

I can add in my hands. Multiplication is addition. Fact. Yet when I have two of anything in my hand and multiple it by zero. I still have two things in my hand. Not zero.

If zero is not "nothing", and I agree, then what is it? It is not a numerical quantity. In fact it is the absence of numerical quantity. So then it is not a number by definitions of numbers. Yet it is also defined as a "whole number".

I shall not continue....I understand how contentious this is for mathematicians.

I think they hate this more than talk of God. Perhaps because it shows the inherent flaws in a system they love so much.

 

[HallsofIvy]

You are confusing two different meanings for the word "slope". In mathematics, the slope of a line is a NUMBER. A number is NOT "vertical".
What do you MEAN by "multiplying" some thing in your hand? 3 times 2 is 6 but if you have two things in you hand and you look at them and THINK I am multiplying this by 3, you still have two things in your hand! Before you can talk about the result of multiplying the two things in your hand by any number, you have to tell us what you are actually doing!
"So then it is not a number by definitions of numbers."
Ah! So the problem is that you do not know what "the definition of numbers" IS!

 

[conway]

You are confusing two different meanings for the word "slope". In mathematics, the slope of a line is a NUMBER. A number is NOT "vertical".
What do you MEAN by "multiplying" some thing in your hand? 3 times 2 is 6 but if you have two things in you hand and you look at them and THINK I am multiplying this by 3, you still have two things in your hand! Before you can talk about the result of multiplying the two things in your hand by any number, you have to tell us what you are actually doing!
"So then it is not a number by definitions of numbers."
Ah! So the problem is that you do not know what "the definition of numbers" IS!

There is no NUMBER to define a vertical slope. There happy? Yet ask any mountain climber if a vertical slope exists, they will say yes. Yet mathematics cannot currently define it.

Semantics is not mathematics...I agree and yield that multiplying, and adding in my hand is semantics not mathematics. Yet philosophically my point remains.

An absract number is defined as a numerical quantity. You have read enough of my post to know, that I know what a number is. A concrete number is defined as a numerical quantity with a unit.

Fact....zero is the "absence" of a numerical quantity. All other numbers are defined as a numerical quantity.

As always you time is greatly appreciated thank you!

 

[HallsofIvy]

Fact....In mathematics, zero is the additive identity in some numeration system. Associating it, or any number, with a "quantity", or lack of "quantity", is an application of mathematics, not mathematics itself.

 

[conway]

https://www.splashlearn.com/math-vocabulary/number-sense/zero#:~:text=Zero is an important number,no amount or null value.

Fact...I am not arguing what the properties of zero are...other than that is is an absence of numerical quantity.

I appreciate our continued conversation.

 

[conway]

I would admit that the link I posted gives a sloppy definition. As we have already both agreed that zero is not "nothing". I was running out of time. Yet the fact I could find such a sloppy definition of zero, is emblematic of the issue that we are discussing. Zero is poorly defined. This is symptomatic of a larger inherent flaw within mathematics.

All bunnies are bunnies because they share "something" in common within the definition of bunnies. Yet zero shares nothing in common with the definition of all other numbers. Nor is its "properties" shared with any other number. Therefore logically is should not be a number. Yet we both agree that it is a number.

This is very easily fixed. Allow all numbers to be composed of numerical quantities, and dimensional quantities. Allow zero to contain a single dimensional quantity. The difference is then that the dimension of zero does not contain a numerical quantity. Zero is empty "space". Yet space is not nothing. Now zero can share something in common with all other numbers. This is the dimensional unit.

Thanks again for your time, and intelligence.

 

[HallsofIvy]

What this is "symptomatic" of is the fact that many people have no idea what mathematics IS. You say "Yet zero shares nothing in common with the definition of all other numbers. Do you even know what that definition is?

 

[conway]

What this is "symptomatic" of is the fact that many people have no idea what mathematics IS. You say "Yet zero shares nothing in common with the definition of all other numbers. Do you even know what that definition is?

I gave a link, to the definition of zero. Perhaps you did not see it.

The truth is, as I can tell from your replies. Is that you do not really want to discuss this. You despise a philosopher "playing" on YOUR playground. I accept that. Ignore me. Have a wonderful new year.

Thank you for what time you did give me!

Just in case I am wrong here....

Show me a single property or definition of zero.....that is also shared with all other numbers...

 

[e.jane.aran]

So if a number has a property that is not shared by *all* other numbers, then that number isn't actually a number? So, since not all integers are even, then 2 can't be a number?

The truth seems to be, as we can see from your replies and your posts, is that you like to play word games, and then appear to get angry when people ask for, or apply, clear definitions.

 

[conway]

All integers are by definition numerical quantities. Therefore they share something in common. So to real's, and imaginary. So to surreal, transfinite, finite, infinitesimals, and infinites. So to every type of number in existence except for zero.

I have not had any angry posts. I have "liked" each response. I have thanked HallsofIvy each and every time for his/her intelligence, and time. As I will do for you.

Literally, each response, has a thank you, and or compliment. Observe for your self.

Thank you for your time!

 

[Antonynguyen]

I also tried entering this problem into the math application and it immediately reported an error. Hah ah

 

[conway]

I also tried entering this problem into the math application and it immediately reported an error. Hah ah

I am not sure I understand you. Are you mocking me, or the idea that division by zero is not definable. I am ok either way, just trying to understand you. In any case I appreciate your time.

 

[Antonynguyen]

I do not mean anything. Sorry

 

[Antonynguyen]

https://www.math-forums.com/threads/multiplication-and-addition.443527/

 

[conway]

https://www.math-forums.com/threads/multiplication-and-addition.443527/

If you have something to add to this conversation, for , or against I am all ears. I suspect you are only trying to garnish views, and posts for this website. Perhaps a bot. I don't know, don't care. Either way I will listen to what you say, even if "off" topic and without direction. Please note for someone like me to make the "claims", that I am making. Is considered absurd by the status quo of mathematcians.

I admit, 99.999 percent of the time, "scientific", or mathematical advancements, comes only from the truly initiated. "As they have earned it". I however have not.

 

[solo_guitar]

1/0=1
1 divided by 0, is 1 divided by nothing.
1 times nothing is nothing 1 time, which is nothing.
1 divided by nothing is 1, because 1 is not divided by anything.
Or am I missing something?[/QUOTE

Never! How can that be?
Division by zero is undefined in mathematics, in life.

Here’s why:

1. Division as the opposite of multiplication: Think of division as the opposite of multiplication.

For example:
12 ÷ 3 = 4 because 4 x 3 = 12

2. Applying this to division by zero: If 1 ÷ 0 = 1, then it should also be true that 1 x 0 = 1.

However, we know that anything multiplied by zero equals zero.

Conclusion: There’s no number you can multiply by zero to get 1.

So, division by zero is undefined or DNE.