# Dividing by Zero

Discussion in 'Basic Math' started by Strontium, Aug 3, 2022.

1. ### Strontium

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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?

Strontium, Aug 3, 2022
2. ### nycmathguy

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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

nycmathguy, Aug 3, 2022
3. ### HallsofIvy

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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".

HallsofIvy, Aug 16, 2022
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4. ### nycmathguy

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nycmathguy, Aug 17, 2022
5. ### conway

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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.

conway, Dec 27, 2023
6. ### HallsofIvy

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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!

HallsofIvy, Dec 31, 2023
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7. ### conway

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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!

conway, Jan 1, 2024
8. ### HallsofIvy

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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.

HallsofIvy, Jan 1, 2024
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9. ### conway

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conway, Jan 1, 2024
10. ### conway

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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.

Last edited: Jan 2, 2024
conway, Jan 2, 2024
11. ### HallsofIvy

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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?

HallsofIvy, Jan 2, 2024
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12. ### conway

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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...

conway, Jan 2, 2024
13. ### e.jane.aran

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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.

e.jane.aran, Jan 3, 2024
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14. ### conway

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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.

conway, Jan 3, 2024
15. ### Antonynguyen

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

Antonynguyen, Jun 21, 2024
16. ### conway

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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.

conway, Jun 21, 2024
17. ### Antonynguyen

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I do not mean anything. Sorry

Antonynguyen, Jun 27, 2024
18. ### Antonynguyen

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Antonynguyen, Jul 1, 2024

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