# 1.2 Defining a proof

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## What are proofs? (informal)

The following submission from an anonymous engineer to the January, 1902 edition of Popular Mechanics caught my eye. Seems like somethingevery Boy/Girl Scout and Architect should know.

HOW TO USE THE WATCH AS A COMPASS: Very few people are aware of the fact that in a watch they are alwaysprovided with a compass, with which, when the sun is shining, the cardinal points can be determined. All one has to do is to point thehour hand to the sun and south is exactly half way between the hour and the figure 12 on the watch. This may seem strange to the averagereader, but it is easily explained. While the sun is passing over 180 degrees (east to west) the hour hand of the watch passes over 360degrees (from 6 o'clock to 6 o'clock). Therefore the angular movement of the sun in one hour corresponds to the angular movement of the hourhand in half an hour; hence, if we point the hour hand toward the sun the line from the point midway between the hour hand and 12 o'clock tothe pivot of the hands will point to the south.Engineer.

They give an argument of correctness; is that really a proof? Well, there are some ambiguities: Do I hold the watch vertically,or, in the plane of the sun's arc? Certainly I can't hold it up-side down, even though this isn't explicitly stated.Furthermore, the correctness of the reasoning relies on some unstated assumptions. E.g. , the sun is at its highest (northernmost) point of its transit at noon.Is this actually true? Does it depend on the time of year?I'm not exactly sure (and will have to sit down and scratch my head and draw pictures of orbits, to convince myself).Certainly there are at least a couple of caveats: even beyond account for Daylight Savings Time,the solar-time and clock-time only align at time-zone boundaries, and they drift up to an hour apart,before the next boundary rectifies the difference. Is this presuming I'm in the northern hemisphere?What if I'm on the equator?

To be fair, the intent of this anecdote was to give enough evidence to convince you,not necessarily to be a complete, stand-alone self-contained proof. But in writing out a careful proof, one is forced to consider all thepoints just made; being forced to understand these can lead you to better understandthe procedure yourself. But be careful to distinguish between something which sounds reasonable,and something that you're certain of.

## An argument by form

How can we tell true proofs from false ones? What, exactly, are the rules of a proof?These are the questions which will occupy us.

Proofs are argument by form. We'll illustrate this with three parallel examples ofa particular proof form called syllogism .

 1 All people are mortal. Premise 2 Socrates is a person. Premise 3 Therefore, Socrates is mortal. Syllogism, lines 1,2
 1 All [substitution ciphers] are [vulnerable to brute-force attacks]. Premise 2 The [Julius Caesar cipher] is a [substitution cipher]. Premise 3 Therefore, the [Julius Caesar cipher] is[vulnerable to brute-force attacks]. Syllogism, lines 1,2

Note that you don't need to know anything about cryptography to know that the conclusion follows from the two premises.(Are the premises indeed true? That's a different question.)

#### Questions & Answers

how can chip be made from sand
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
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