Nill - Revision history

Lfox: /* Examples */

2024-02-14T03:26:53Z

Examples

← Older revision		Revision as of 03:26, 14 February 2024
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	== Examples ==		== Examples ==

	=== Examples ===		=== Examples of negligible nill ===
	If a piece of paper is being considered in a context where one is measuring skyscrapers, its thickness is nill. The amount by which a piece of paper placed on top of a skyscraper augments its height is completely negligible.		If a piece of paper is being considered in a context where one is measuring skyscrapers, its thickness is nill. The amount by which a piece of paper placed on top of a skyscraper augments its height is completely negligible.

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	Gas stations sometimes charge amounts of USD which are more precise than 1 cent, despite the fact that 1 cent is the lowest denomination of US currency. E.g. gas might be worth $3.782 per gallon. What this really means is that, when the customer has finished filling his car with gas, the amount charged to the customer is rounded to the nearest cent. For example, at the aforementioned price, if the customer purchases 13 gallons of gas, he will be charged $49.17, rather than $49.166 = 13 * $3.782. In this context, we say that any amount charged which is below $0.01 is nill.		Gas stations sometimes charge amounts of USD which are more precise than 1 cent, despite the fact that 1 cent is the lowest denomination of US currency. E.g. gas might be worth $3.782 per gallon. What this really means is that, when the customer has finished filling his car with gas, the amount charged to the customer is rounded to the nearest cent. For example, at the aforementioned price, if the customer purchases 13 gallons of gas, he will be charged $49.17, rather than $49.166 = 13 * $3.782. In this context, we say that any amount charged which is below $0.01 is nill.

			=== Examples of unmeasurable nill ===
			I cannot tell the difference between a 120Hz display and a 240Hz display, so in the context of human perception, the nill interval for time should be about 1/120 seconds, or 0.0083 seconds.

			In a context where one is using a 1000x visible light microscope, I expect that the nill interval for length should be about 0.1 micrometers.

			At 1m distance, I cannot see things which are much smaller than the width of a human hair, so in that context, the nill interval for length should be about 0.1 millimeters.

			I can definitely hear the difference between a tone of 450Hz and a tone of 455Hz, but I definitely cannot hear the difference between a tone of 450Hz and 451Hz. Therefore, I estimate that in the context of human perception of tone, the nill interval should be about 1Hz.

	=== Non-examples ===		=== Non-examples ===

Lfox at 02:11, 14 February 2024

2024-02-14T02:11:11Z

← Older revision		Revision as of 02:11, 14 February 2024
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	Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of [[Integers\|zero]], but is not the same.		Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of [[Integers\|zero]], but is not the same.

	[TODO: I think that the concept nill should mean it's so small that it's not measurable at all. This means you can't even see it. It's smaller than just whatever margin of error is on your ruler.]		[TODO: I think that the concept nill should mean it's so small that it's not measurable at all. This means you can't even see it. It's smaller than just whatever margin of error is on your ruler. I need more concepts than just this though, because there's also an idea of something which is perceptible but within "margin of error" of 0. There's also an idea of something which perfectly measurable, but is negligible in the present context, like the width of a piece of paper.]

	== Examples ==		== Examples ==

Lfox at 02:06, 14 February 2024

2024-02-14T02:06:56Z

← Older revision		Revision as of 02:06, 14 February 2024
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	Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of [[Integers\|zero]], but is not the same.		Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of [[Integers\|zero]], but is not the same.

			[TODO: I think that the concept nill should mean it's so small that it's not measurable at all. This means you can't even see it. It's smaller than just whatever margin of error is on your ruler.]

	== Examples ==		== Examples ==

Lfox at 22:48, 28 January 2024

2024-01-28T22:48:42Z

← Older revision		Revision as of 22:48, 28 January 2024
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	=== Non-examples ===		=== Non-examples ===
	In the context where a piece of paper is considered together with the hundreds of other pages of a book, the thickness of a piece of paper is not nill.		In the context where a piece of paper is considered together with the hundreds of other pages of a book, the thickness of a piece of paper is not nill.

			== Nill cutoff ==
			One way of using the concept of nill in mathematics to introduce nill cutoff, i.e. a concrete number <math>\nu : \mathbb{Q}_{>0}</math>, such that any <math>x : \mathbb{Q}</math> such that <math>\|x\| < \nu </math> is considered to be nill.

	== Contrast with infinitesimal ==		== Contrast with infinitesimal ==

Lfox: /* Contrast with infinitesimal */

2024-01-27T23:39:01Z

Contrast with infinitesimal

← Older revision		Revision as of 23:39, 27 January 2024
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	== Contrast with infinitesimal ==		== Contrast with infinitesimal ==
	If a large number of nill quantities are added together, the resulting quantity will not necessarily be nill.		If a large number of nill quantities are added together, the resulting quantity will not necessarily be nill. This is unlike infinitesimals; a finite sum of infinitely small things is still supposed to be infinitely small.

	== References ==		== References ==
	The name nill for this concept was coined by Harry Binswanger in his lecture [https://www.youtube.com/watch?v=GwHAObb7tt8 Saving Math from Plato]. [TODO rephrase or put this elsewhere in the document]		The name nill for this concept was coined by Harry Binswanger in his lecture [https://www.youtube.com/watch?v=GwHAObb7tt8 Saving Math from Plato]. [TODO rephrase or put this elsewhere in the document]

Lfox: /* Examples */

2024-01-27T02:55:11Z

Examples

← Older revision		Revision as of 02:55, 27 January 2024
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	=== Examples ===		=== Examples ===
	~~In the~~ context where [...], the ~~thickness~~ of ~~a piece~~ of ~~paper~~ is nill.		If a piece of paper is being considered in a context where one is measuring skyscrapers, its thickness is nill. The amount by which a piece of paper placed on top of a skyscraper augments its height is completely negligible.

			If a scale measures weight in units of 0.1 pounds, then any object weighing much less than 0.1 pounds has nill weight.

			Gas stations sometimes charge amounts of USD which are more precise than 1 cent, despite the fact that 1 cent is the lowest denomination of US currency. E.g. gas might be worth $3.782 per gallon. What this really means is that, when the customer has finished filling his car with gas, the amount charged to the customer is rounded to the nearest cent. For example, at the aforementioned price, if the customer purchases 13 gallons of gas, he will be charged $49.17, rather than $49.166 = 13 * $3.782. In this context, we say that any amount charged which is below $0.01 is nill.

	=== Non-examples ===		=== Non-examples ===

Lfox at 20:31, 26 January 2024

2024-01-26T20:31:27Z

← Older revision		Revision as of 20:31, 26 January 2024
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	A quantity is said to be '''nill''', or '''negligible''', if it is small enough that it can be ignored~~. Nill presupposes a given~~ context.		A quantity is said to be '''nill''', or '''negligible''', if it is small enough that it can be ignored in the present context.

	Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of [[Integers\|zero]], but is not the same.		Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of [[Integers\|zero]], but is not the same.

			== Examples ==

			=== Examples ===
			In the context where [...], the thickness of a piece of paper is nill.

			=== Non-examples ===
			In the context where a piece of paper is considered together with the hundreds of other pages of a book, the thickness of a piece of paper is not nill.

			== Contrast with infinitesimal ==
			If a large number of nill quantities are added together, the resulting quantity will not necessarily be nill.

	== References ==		== References ==
	The name nill for this concept was coined by Harry Binswanger in his lecture [https://www.youtube.com/watch?v=GwHAObb7tt8 Saving Math from Plato]. [TODO rephrase or put this elsewhere in the document]		The name nill for this concept was coined by Harry Binswanger in his lecture [https://www.youtube.com/watch?v=GwHAObb7tt8 Saving Math from Plato]. [TODO rephrase or put this elsewhere in the document]

Lfox at 04:32, 21 January 2024

2024-01-21T04:32:10Z

← Older revision		Revision as of 04:32, 21 January 2024
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	A quantity is said to be '''nill''', or '''negligible''', if it is small enough that it can be ignored. Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of [[Integers\|zero]], but is not the same.		A quantity is said to be '''nill''', or '''negligible''', if it is small enough that it can be ignored. Nill presupposes a given context.

			Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of [[Integers\|zero]], but is not the same.

	== References ==		== References ==
	The name nill for this concept was coined by Harry Binswanger in his lecture [https://www.youtube.com/watch?v=GwHAObb7tt8 Saving Math from Plato]. [TODO rephrase or put this elsewhere in the document]		The name nill for this concept was coined by Harry Binswanger in his lecture [https://www.youtube.com/watch?v=GwHAObb7tt8 Saving Math from Plato]. [TODO rephrase or put this elsewhere in the document]

Lfox: Created page with "A quantity is said to be '''nill''', or '''negligible''', if it is small enough that it can be ignored. Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of zero, but is not the same. == References == The name nill for this concept was coined by Harry Binswanger in his lecture [https://www.youtube.com/watch?v=GwHAObb7tt8 Saving Math from Plato]. [TODO r..."

2024-01-21T04:30:38Z

Created page with "A quantity is said to be '''nill''', or '''negligible''', if it is small enough that it can be ignored. Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of zero, but is not the same. == References == The name nill for this concept was coined by Harry Binswanger in his lecture [https://www.youtube.com/watch?v=GwHAObb7tt8 Saving Math from Plato]. [TODO r..."

New page

A quantity is said to be '''nill''', or '''negligible''', if it is small enough that it can be ignored. Nill is closely related to the standard mathematics concept of an '''infinitesimal''', but it is not the same. Nill is also closely related to the concept of [[Integers|zero]], but is not the same.

== References ==
The name nill for this concept was coined by Harry Binswanger in his lecture [https://www.youtube.com/watch?v=GwHAObb7tt8 Saving Math from Plato]. [TODO rephrase or put this elsewhere in the document]