How a false math proof can teach us a simple truth

Realizing DevOps on the Mainframe and achieving greater business agility comes from wanting more for less.

A fun proof for all math geeks

1+1=3. True statement or false? In reliving some of my formative years as bona fide math geek, I decided to showcase this “magic trick” at a recent family dinner. It’s a variant of the more commonly known 2=1 proof, see if you can spot the problem below!

Let a and b be equal, non-zero quantities

(1)   a = b (multiply by a)

(2)   a2 = a*b (subtract by b2)

(3)   a2 – b2 = ab – b2 (factor both sides)

(4)   (a + b)*(a – b) = b*(a – b) (divide by a – b)

(5)   a + b = b (observing that a = b)

(6)   b + b = b (combine and divide by non-zero b)

(7)   2 = 1

Like any good magic trick, it left many unsuspecting guests quite bewildered at reality revealed in front of them. And like any good magician, I was also sure to apply subtle misdirection from the real culprit, a divide by zero error on line 4 that in the world of mathematics means you simply cannot get something for nothing.

So what does 1+1=3 teach us?

While 1+1=3 is not a true statement, it nicely embodies the desire to achieve more for less. I first came across this notion at the INBOUND 2012 keynote, in which 1+1=3 was used to describe the revolutionary benefits brought by the iPhone. The device includes an email and camera function, providing benefits represented by the two 1’s on the left hand side, and moreover, an additional “hidden” 1 from their combined ability to allow a customer to take a photo and immediately share it via email.

This feature integration has forever changed how customers utilize smartphones, and in that vein, the analogy speaks volumes to the latent value of DevOps. A DevOps implementation already drives value from interplay between and new collaboration between development and operations, but the real kicker comes from the net new value derived from shifting left to embed operations further into the development cycle, which in turn drives business agility and more frequent code release cycles.

Building the path to greater business agility

Business Agility is a core focus for CA Mainframe solutions. And we’re serious about helping customers achieve this. Using our solutions:

  • CA helps customers deliver code more frequently, at higher quality

o   64 percent of customers say CA Application Development software helps them deliver code more frequently[1]

o   65 percent of customers say CA Application Development software helps them deliver higher quality software[2]

  • CA helps customers to drive revenue and save costs while automating workloads

o   Customers implementing CA Workload Automation can achieve up to 22.5 percent incremental revenue and a 50 percent reduction in workload management efforts

  • CA helps deliver improved monitoring and visibility mobile to mainframe

o   A large bank was able to deliver rapid innovation to customers despite multiple non-integrated solutions with CA Application Lifecycle Conductor

o   Another banking customer saved $450k over three years with proactive incident detection with CA Cross-Enterprise APM

We feel that as a result of this and our ongoing commitment to customers, we are now leading in market share revenue for Application Development Mainframe Tools and IT Operations Mainframe Tools, worldwide as indicated by the latest market share update, Market Share: All Software Markets, Worldwide, 2015 report published on March 31, 2016 by Gartner.

What do you think is the first step for your organization to achieve greater business agility? Please leave your feedback below, and let us know what you think about our evolving story in Mainframe Application Development and IT Operations.

Charts created by CA Technologies based on Gartner research. Source: Gartner, Inc., Market Share: All Software Markets, Worldwide, 2015, Hai H. Swinehart, et al, March 31, 2016.


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[1] Source: TechValidate. TVID: 65B-E99-036

[2] Source: TechValidate. TVID: BF9-0EB-589

Marvin leads product marketing for the CA Mainframe Application Development portfolio, and supports the BU…



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